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Commit f5103a6c authored by Radek Fučík's avatar Radek Fučík
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added txt outputs from supp materials 

Changes to be committed:
	new file:   supp_d1q3_ade_txt/output_d1q3_ade_clbm1_symbolic_pde_00.txt
	new file:   supp_d1q3_ade_txt/output_d1q3_ade_mrt1_symbolic_pde_00.txt
	new file:   supp_d1q3_ade_txt/output_d1q3_ade_srt_symbolic_pde_00.txt
	new file:   supp_d1q3_nse_txt/output_d1q3_nse_clbm1_symbolic_pde_00.txt
	new file:   supp_d1q3_nse_txt/output_d1q3_nse_clbm1_symbolic_pde_01.txt
	new file:   supp_d1q3_nse_txt/output_d1q3_nse_mrt1_symbolic_pde_00.txt
	new file:   supp_d1q3_nse_txt/output_d1q3_nse_mrt1_symbolic_pde_01.txt
	new file:   supp_d1q3_nse_txt/output_d1q3_nse_srt_symbolic_pde_00.txt
	new file:   supp_d1q3_nse_txt/output_d1q3_nse_srt_symbolic_pde_01.txt
	new file:   supp_d2q5_ade_txt/output_d2q5_ade_clbm1_symbolic_pde_00.txt
	new file:   supp_d2q5_ade_txt/output_d2q5_ade_clbm2_symbolic_pde_00.txt
	new file:   supp_d2q5_ade_txt/output_d2q5_ade_mrt1_symbolic_pde_00.txt
	new file:   supp_d2q5_ade_txt/output_d2q5_ade_mrt2_symbolic_pde_00.txt
	new file:   supp_d2q5_ade_txt/output_d2q5_ade_srt_symbolic_pde_00.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_clbm1_symbolic_pde_00.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_clbm1_symbolic_pde_01.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_clbm1_symbolic_pde_02.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_clbm2_symbolic_pde_00.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_clbm2_symbolic_pde_01.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_clbm2_symbolic_pde_02.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_culbm1_symbolic_pde_00.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_culbm1_symbolic_pde_01.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_culbm1_symbolic_pde_02.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_culbm2_symbolic_pde_00.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_culbm2_symbolic_pde_01.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_culbm2_symbolic_pde_02.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_mrt1_symbolic_pde_00.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_mrt1_symbolic_pde_01.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_mrt1_symbolic_pde_02.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_mrt2_symbolic_pde_00.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_mrt2_symbolic_pde_01.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_mrt2_symbolic_pde_02.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_srt_symbolic_pde_00.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_srt_symbolic_pde_01.txt
	new file:   supp_d2q9_nse_txt/output_d2q9_nse_srt_symbolic_pde_02.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_clbm1_symbolic_pde_00.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_clbm1_symbolic_pde_01.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_clbm1_symbolic_pde_02.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_clbm1_symbolic_pde_03.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_clbm2_symbolic_pde_00.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_clbm2_symbolic_pde_01.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_clbm2_symbolic_pde_02.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_clbm2_symbolic_pde_03.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_culbm1_symbolic_pde_00.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_culbm1_symbolic_pde_01.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_culbm1_symbolic_pde_02.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_culbm1_symbolic_pde_03.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_culbm2_symbolic_pde_00.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_culbm2_symbolic_pde_01.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_culbm2_symbolic_pde_02.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_culbm2_symbolic_pde_03.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_mrt1_symbolic_pde_00.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_mrt1_symbolic_pde_01.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_mrt1_symbolic_pde_02.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_mrt1_symbolic_pde_03.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_mrt2_symbolic_pde_00.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_mrt2_symbolic_pde_01.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_mrt2_symbolic_pde_02.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_mrt2_symbolic_pde_03.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_srt_symbolic_pde_00.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_srt_symbolic_pde_01.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_srt_symbolic_pde_02.txt
	new file:   supp_d3q27_nse_txt/output_d3q27_nse_srt_symbolic_pde_03.txt
	new file:   supp_d3q7_ade_txt/output_d3q7_ade_clbm1_symbolic_pde_00.txt
	new file:   supp_d3q7_ade_txt/output_d3q7_ade_clbm2_symbolic_pde_00.txt
	new file:   supp_d3q7_ade_txt/output_d3q7_ade_mrt1_symbolic_pde_00.txt
	new file:   supp_d3q7_ade_txt/output_d3q7_ade_mrt2_symbolic_pde_00.txt
	new file:   supp_d3q7_ade_txt/output_d3q7_ade_srt_symbolic_pde_00.txt
parent da3f1cdf
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Inline Side-by-side
supp_d1q3_ade_txt/output_d1q3_ade_clbm1_symbolic_pde_00.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
D[0](rho)(t,x,y,z)-1/2*D[1](u)(t,x,y,z)^2*(2*dl^2*dt^(-1)*rho(t,x,y,z)*omega_2^(-1)-dl^2*dt^(-1)*rho(t,x,y,z))-1/2*D[0,0,0,1](u)(t,x,y,z)*(dl*dt^2*rho(t,x,y,z)*omega_2^(-1)+2*dl*dt^2*rho(t,x,y,z)*omega_2^(-3)-3*dl*dt^2*rho(t,x,y,z)*omega_2^(-2))+dl*D[1](u)(t,x,y,z)*dt^(-1)*rho(t,x,y,z)+1/6*D[0,1,1](u)(t,x,y,z)*(12*dl^2*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-2)-12*dl^2*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-1)+dl^2*rho(t,x,y,z)*u(t,x,y,z))-1/2*D[1,1](u)(t,x,y,z)*(2*dl^2*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-1)-dl^2*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z))+3/2*D[0,0,1,1](u)(t,x,y,z)*(3*dl^2*dt*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-2)-2*dl^2*dt*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-3)-dl^2*dt*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-1))+1/12*D[1,1,1,1](u)(t,x,y,z)*(2*dl^4*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3+42*dl^4*omega_3^(-2)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3-84*dl^4*omega_3^(-2)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*omega_2^(-1)+2*dl^4*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*omega_2^(-1)-12*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-2)+24*dl^4*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*omega_2^(-1)-30*dl^4*dt^(-1)*c_s^2*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-2)+6*dl^4*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-2)-18*dl^4*omega_3^(-2)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)-dl^4*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)+24*dl^4*dt^(-1)*c_s^2*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-3)-12*dl^4*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-2)-24*dl^4*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-1)-24*dl^4*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3+2*dl^4*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-1)+36*dl^4*omega_3^(-2)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-1)-60*dl^4*omega_3^(-2)*dt^(-1)*c_s^2*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-1)-2*dl^4*dt^(-1)*c_s^2*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-1)+12*dl^4*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)-12*dl^4*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*omega_2^(-3)+72*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*rho(t,x,y,z)*u(t,x,y,z)*omega_2^(-1)+30*dl^4*omega_3^(-2)*dt^(-1)*c_s^2*rho(t,x,y,z)*u(t,x,y,z)+dl^4*dt^(-1)*c_s^2*rho(t,x,y,z)*u(t,x,y,z)+60*dl^4*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*omega_2^(-2)-24*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*rho(t,x,y,z)*u(t,x,y,z)-12*dl^4*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*omega_2^(-2))+1/12*D[0,0,1](u)(t,x,y,z)*(12*dl*dt*rho(t,x,y,z)*omega_2^(-2)-12*dl*dt*rho(t,x,y,z)*omega_2^(-1)+dl*dt*rho(t,x,y,z))-1/2*D[0,1](u)(t,x,y,z)*(2*dl*rho(t,x,y,z)*omega_2^(-1)-dl*rho(t,x,y,z))-1/24*D[1,1,1,1](rho)(t,x,y,z)*(30*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^4-24*dl^4*dt^(-1)*c_s^4*omega_2^(-3)+24*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*omega_2^(-2)-72*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^4*omega_2^(-1)+36*dl^4*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^2-12*dl^4*dt^(-1)*u(t,x,y,z)^2*omega_2^(-1)-72*dl^4*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^2*omega_2^(-1)+48*dl^4*dt^(-1)*c_s^4*omega_2^(-2)-dl^4*dt^(-1)*c_s^2+24*dl^4*omega_3^(-1)*dt^(-1)*c_s^4*omega_2^(-1)+72*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*u(t,x,y,z)^2-3*dl^4*dt^(-1)*u(t,x,y,z)^4+36*dl^4*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-2)-72*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-2)+8*dl^4*dt^(-1)*c_s^2*omega_2^(-1)+6*dl^4*omega_3^(-1)*dt^(-1)*c_s^2+72*dl^4*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^4*omega_2^(-1)+12*dl^4*dt^(-1)*u(t,x,y,z)^4*omega_2^(-1)-12*dl^4*dt^(-1)*c_s^2*omega_2^(-2)-144*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-1)+3*dl^4*dt^(-1)*u(t,x,y,z)^2-6*dl^4*omega_3^(-1)*dt^(-1)*c_s^4+216*dl^4*omega_3^(-2)*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-1)+12*dl^4*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-1)-24*dl^4*omega_3^(-1)*dt^(-1)*c_s^4*omega_2^(-2)+72*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*omega_2^(-1)-36*dl^4*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^4-30*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2-24*dl^4*dt^(-1)*c_s^4*omega_2^(-1)-6*dl^4*dt^(-1)*c_s^2*u(t,x,y,z)^2-108*dl^4*omega_3^(-2)*dt^(-1)*c_s^2*u(t,x,y,z)^2-24*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*omega_2^(-1)+3*dl^4*dt^(-1)*c_s^4)-1/2*D[1](rho)(t,x,y,z)*(2*dl^2*dt^(-1)*u(t,x,y,z)*omega_2^(-1)-dl^2*dt^(-1)*u(t,x,y,z))*D[1](u)(t,x,y,z)+1/6*D[1,1,1](rho)(t,x,y,z)*(dl^3*dt^(-1)*u(t,x,y,z)+3*dl^3*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3-3*dl^3*dt^(-1)*u(t,x,y,z)*omega_2^(-1)-6*dl^3*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3*omega_2^(-1)-3*dl^3*omega_3^(-1)*dt^(-1)*u(t,x,y,z)-dl^3*dt^(-1)*u(t,x,y,z)^3-3*dl^3*dt^(-1)*c_s^2*u(t,x,y,z)+9*dl^3*dt^(-1)*c_s^2*u(t,x,y,z)*omega_2^(-1)+6*dl^3*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*omega_2^(-1)+3*dl^3*dt^(-1)*u(t,x,y,z)^3*omega_2^(-1)-18*dl^3*omega_3^(-1)*dt^(-1)*c_s^2*u(t,x,y,z)*omega_2^(-1)+9*dl^3*omega_3^(-1)*dt^(-1)*c_s^2*u(t,x,y,z))+D[1](rho)(t,x,y,z)*dl*dt^(-1)*u(t,x,y,z)+1/2*D[1](rho)(t,x,y,z)*(dl-2*dl*omega_2^(-1))*D[0](u)(t,x,y,z)-1/12*D[1,1,1](u)(t,x,y,z)*(12*dl^3*dt^(-1)*c_s^2*rho(t,x,y,z)*omega_2^(-2)-2*dl^3*dt^(-1)*rho(t,x,y,z)+6*dl^3*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)+6*dl^3*dt^(-1)*rho(t,x,y,z)*omega_2^(-1)+3*dl^3*dt^(-1)*c_s^2*rho(t,x,y,z)-12*dl^3*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*omega_2^(-2)-18*dl^3*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2-6*dl^3*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*omega_2^(-1)+12*dl^3*omega_3^(-1)*dt^(-1)*c_s^2*rho(t,x,y,z)*omega_2^(-1)-18*dl^3*dt^(-1)*c_s^2*rho(t,x,y,z)*omega_2^(-1)+5*dl^3*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2-12*dl^3*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*omega_2^(-1)-6*dl^3*omega_3^(-1)*dt^(-1)*c_s^2*rho(t,x,y,z)+36*dl^3*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*omega_2^(-1))+1/2*D[1,1](rho)(t,x,y,z)*(dl^2*dt^(-1)*c_s^2-2*dl^2*dt^(-1)*c_s^2*omega_2^(-1))-1/12*D[0,1,1,1](u)(t,x,y,z)*(3*dl^3*rho(t,x,y,z)*u(t,x,y,z)^2+24*dl^3*omega_3^(-1)*rho(t,x,y,z)*omega_2^(-2)-15*dl^3*rho(t,x,y,z)*u(t,x,y,z)^2*omega_2^(-1)-24*dl^3*omega_3^(-1)*c_s^2*rho(t,x,y,z)*omega_2^(-2)+12*dl^3*omega_3^(-2)*rho(t,x,y,z)*omega_2^(-1)+6*dl^3*omega_3^(-2)*c_s^2*rho(t,x,y,z)-36*dl^3*omega_3^(-2)*rho(t,x,y,z)*u(t,x,y,z)^2*omega_2^(-1)-72*dl^3*omega_3^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*omega_2^(-2)-25*dl^3*c_s^2*rho(t,x,y,z)*omega_2^(-1)-12*dl^3*rho(t,x,y,z)*omega_2^(-2)-dl^3*rho(t,x,y,z)-27*dl^3*omega_3^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2+9*dl^3*omega_3^(-1)*rho(t,x,y,z)-12*dl^3*omega_3^(-2)*c_s^2*rho(t,x,y,z)*omega_2^(-1)-24*dl^3*c_s^2*rho(t,x,y,z)*omega_2^(-3)-6*dl^3*omega_3^(-2)*rho(t,x,y,z)+18*dl^3*omega_3^(-2)*rho(t,x,y,z)*u(t,x,y,z)^2+108*dl^3*omega_3^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*omega_2^(-1)+2*dl^3*c_s^2*rho(t,x,y,z)+11*dl^3*rho(t,x,y,z)*omega_2^(-1)+48*dl^3*c_s^2*rho(t,x,y,z)*omega_2^(-2)+36*dl^3*rho(t,x,y,z)*u(t,x,y,z)^2*omega_2^(-3)-18*dl^3*rho(t,x,y,z)*u(t,x,y,z)^2*omega_2^(-2)+36*dl^3*omega_3^(-1)*c_s^2*rho(t,x,y,z)*omega_2^(-1)-9*dl^3*omega_3^(-1)*c_s^2*rho(t,x,y,z)-36*dl^3*omega_3^(-1)*rho(t,x,y,z)*omega_2^(-1))=0
List of all coefficients of each partial derivatives:
D[1](rho)
dl*dt^(-1)*u
D[1](u)
dl*dt^(-1)*rho
D[0](rho)
1
D[1,1](rho)
1/2*dl^2*dt^(-1)*c_s^2-dl^2*dt^(-1)*c_s^2*omega_2^(-1)
D[1,1](u)
-dl^2*dt^(-1)*rho*u*omega_2^(-1)+1/2*dl^2*dt^(-1)*rho*u
D[0,1](u)
-dl*rho*omega_2^(-1)+1/2*dl*rho
D[1,1,1](rho)
1/6*dl^3*dt^(-1)*u+1/2*dl^3*omega_3^(-1)*dt^(-1)*u^3-1/2*dl^3*dt^(-1)*u*omega_2^(-1)-dl^3*omega_3^(-1)*dt^(-1)*u^3*omega_2^(-1)-1/2*dl^3*omega_3^(-1)*dt^(-1)*u-1/6*dl^3*dt^(-1)*u^3-1/2*dl^3*dt^(-1)*c_s^2*u+3/2*dl^3*dt^(-1)*c_s^2*u*omega_2^(-1)+dl^3*omega_3^(-1)*dt^(-1)*u*omega_2^(-1)+1/2*dl^3*dt^(-1)*u^3*omega_2^(-1)-3*dl^3*omega_3^(-1)*dt^(-1)*c_s^2*u*omega_2^(-1)+3/2*dl^3*omega_3^(-1)*dt^(-1)*c_s^2*u
D[1,1,1](u)
-dl^3*dt^(-1)*c_s^2*rho*omega_2^(-2)+1/6*dl^3*dt^(-1)*rho-1/2*dl^3*omega_3^(-1)*dt^(-1)*rho-1/2*dl^3*dt^(-1)*rho*omega_2^(-1)-1/4*dl^3*dt^(-1)*c_s^2*rho+dl^3*dt^(-1)*rho*u^2*omega_2^(-2)+3/2*dl^3*omega_3^(-1)*dt^(-1)*rho*u^2+1/2*dl^3*dt^(-1)*rho*u^2*omega_2^(-1)-dl^3*omega_3^(-1)*dt^(-1)*c_s^2*rho*omega_2^(-1)+3/2*dl^3*dt^(-1)*c_s^2*rho*omega_2^(-1)-5/12*dl^3*dt^(-1)*rho*u^2+dl^3*omega_3^(-1)*dt^(-1)*rho*omega_2^(-1)+1/2*dl^3*omega_3^(-1)*dt^(-1)*c_s^2*rho-3*dl^3*omega_3^(-1)*dt^(-1)*rho*u^2*omega_2^(-1)
D[0,1,1](u)
2*dl^2*rho*u*omega_2^(-2)-2*dl^2*rho*u*omega_2^(-1)+1/6*dl^2*rho*u
D[0,0,1](u)
dl*dt*rho*omega_2^(-2)-dl*dt*rho*omega_2^(-1)+1/12*dl*dt*rho
D[1,1,1,1](rho)
-5/4*dl^4*omega_3^(-1)*dt^(-1)*u^4+dl^4*dt^(-1)*c_s^4*omega_2^(-3)-dl^4*omega_3^(-1)*dt^(-1)*c_s^2*omega_2^(-2)+3*dl^4*omega_3^(-1)*dt^(-1)*u^4*omega_2^(-1)-3/2*dl^4*omega_3^(-2)*dt^(-1)*u^2+1/2*dl^4*dt^(-1)*u^2*omega_2^(-1)+3*dl^4*omega_3^(-2)*dt^(-1)*u^2*omega_2^(-1)-2*dl^4*dt^(-1)*c_s^4*omega_2^(-2)+1/24*dl^4*dt^(-1)*c_s^2-dl^4*omega_3^(-1)*dt^(-1)*c_s^4*omega_2^(-1)-3*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*u^2+1/8*dl^4*dt^(-1)*u^4-3/2*dl^4*dt^(-1)*c_s^2*u^2*omega_2^(-2)+3*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*u^2*omega_2^(-2)-1/3*dl^4*dt^(-1)*c_s^2*omega_2^(-1)-1/4*dl^4*omega_3^(-1)*dt^(-1)*c_s^2-3*dl^4*omega_3^(-2)*dt^(-1)*u^4*omega_2^(-1)-1/2*dl^4*dt^(-1)*u^4*omega_2^(-1)+1/2*dl^4*dt^(-1)*c_s^2*omega_2^(-2)+6*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*u^2*omega_2^(-1)-1/8*dl^4*dt^(-1)*u^2+1/4*dl^4*omega_3^(-1)*dt^(-1)*c_s^4-9*dl^4*omega_3^(-2)*dt^(-1)*c_s^2*u^2*omega_2^(-1)-1/2*dl^4*dt^(-1)*c_s^2*u^2*omega_2^(-1)+dl^4*omega_3^(-1)*dt^(-1)*c_s^4*omega_2^(-2)-3*dl^4*omega_3^(-1)*dt^(-1)*u^2*omega_2^(-1)+3/2*dl^4*omega_3^(-2)*dt^(-1)*u^4+5/4*dl^4*omega_3^(-1)*dt^(-1)*u^2+dl^4*dt^(-1)*c_s^4*omega_2^(-1)+1/4*dl^4*dt^(-1)*c_s^2*u^2+9/2*dl^4*omega_3^(-2)*dt^(-1)*c_s^2*u^2+dl^4*omega_3^(-1)*dt^(-1)*c_s^2*omega_2^(-1)-1/8*dl^4*dt^(-1)*c_s^4
D[1,1,1,1](u)
1/6*dl^4*dt^(-1)*rho*u^3+7/2*dl^4*omega_3^(-2)*dt^(-1)*rho*u^3-7*dl^4*omega_3^(-2)*dt^(-1)*rho*u^3*omega_2^(-1)+1/6*dl^4*dt^(-1)*rho*u^3*omega_2^(-1)-dl^4*omega_3^(-1)*dt^(-1)*c_s^2*rho*u*omega_2^(-2)+2*dl^4*omega_3^(-1)*dt^(-1)*rho*u^3*omega_2^(-1)-5/2*dl^4*dt^(-1)*c_s^2*rho*u*omega_2^(-2)+1/2*dl^4*dt^(-1)*rho*u*omega_2^(-2)-3/2*dl^4*omega_3^(-2)*dt^(-1)*rho*u-1/12*dl^4*dt^(-1)*rho*u+2*dl^4*dt^(-1)*c_s^2*rho*u*omega_2^(-3)-dl^4*omega_3^(-1)*dt^(-1)*rho*u*omega_2^(-2)-2*dl^4*omega_3^(-1)*dt^(-1)*rho*u*omega_2^(-1)-2*dl^4*omega_3^(-1)*dt^(-1)*rho*u^3+1/6*dl^4*dt^(-1)*rho*u*omega_2^(-1)+3*dl^4*omega_3^(-2)*dt^(-1)*rho*u*omega_2^(-1)-5*dl^4*omega_3^(-2)*dt^(-1)*c_s^2*rho*u*omega_2^(-1)-1/6*dl^4*dt^(-1)*c_s^2*rho*u*omega_2^(-1)+dl^4*omega_3^(-1)*dt^(-1)*rho*u-dl^4*dt^(-1)*rho*u^3*omega_2^(-3)+6*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*rho*u*omega_2^(-1)+5/2*dl^4*omega_3^(-2)*dt^(-1)*c_s^2*rho*u+1/12*dl^4*dt^(-1)*c_s^2*rho*u+5*dl^4*omega_3^(-1)*dt^(-1)*rho*u^3*omega_2^(-2)-2*dl^4*omega_3^(-1)*dt^(-1)*c_s^2*rho*u-dl^4*dt^(-1)*rho*u^3*omega_2^(-2)
D[0,1,1,1](u)
-1/4*dl^3*rho*u^2-2*dl^3*omega_3^(-1)*rho*omega_2^(-2)+5/4*dl^3*rho*u^2*omega_2^(-1)+2*dl^3*omega_3^(-1)*c_s^2*rho*omega_2^(-2)-dl^3*omega_3^(-2)*rho*omega_2^(-1)-1/2*dl^3*omega_3^(-2)*c_s^2*rho+3*dl^3*omega_3^(-2)*rho*u^2*omega_2^(-1)+6*dl^3*omega_3^(-1)*rho*u^2*omega_2^(-2)+25/12*dl^3*c_s^2*rho*omega_2^(-1)+dl^3*rho*omega_2^(-2)+1/12*dl^3*rho+9/4*dl^3*omega_3^(-1)*rho*u^2-3/4*dl^3*omega_3^(-1)*rho+dl^3*omega_3^(-2)*c_s^2*rho*omega_2^(-1)+2*dl^3*c_s^2*rho*omega_2^(-3)+1/2*dl^3*omega_3^(-2)*rho-3/2*dl^3*omega_3^(-2)*rho*u^2-9*dl^3*omega_3^(-1)*rho*u^2*omega_2^(-1)-1/6*dl^3*c_s^2*rho-11/12*dl^3*rho*omega_2^(-1)-4*dl^3*c_s^2*rho*omega_2^(-2)-3*dl^3*rho*u^2*omega_2^(-3)+3/2*dl^3*rho*u^2*omega_2^(-2)-3*dl^3*omega_3^(-1)*c_s^2*rho*omega_2^(-1)+3/4*dl^3*omega_3^(-1)*c_s^2*rho+3*dl^3*omega_3^(-1)*rho*omega_2^(-1)
D[0,0,1,1](u)
9/2*dl^2*dt*rho*u*omega_2^(-2)-3*dl^2*dt*rho*u*omega_2^(-3)-3/2*dl^2*dt*rho*u*omega_2^(-1)
D[0,0,0,1](u)
-1/2*dl*dt^2*rho*omega_2^(-1)-dl*dt^2*rho*omega_2^(-3)+3/2*dl*dt^2*rho*omega_2^(-2)
D[1](rho) * D[1](u)
-dl^2*dt^(-1)*u*omega_2^(-1)+1/2*dl^2*dt^(-1)*u
D[1](u) * D[1](u)
-dl^2*dt^(-1)*rho*omega_2^(-1)+1/2*dl^2*dt^(-1)*rho
D[1](rho) * D[0](u)
1/2*dl-dl*omega_2^(-1)
supp_d1q3_ade_txt/output_d1q3_ade_mrt1_symbolic_pde_00.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
1/2*(dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^2-2*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^2)*D[1,1](u)(t,x,y,z)-1/2*D[0](u)(t,x,y,z)*D[1](rho)(t,x,y,z)*(2*omega_2^(-1)*dl-dl)-1/2*D[1,1](rho)(t,x,y,z)*(2*dt^(-1)*c_s^2*omega_2^(-1)*dl^2-dt^(-1)*c_s^2*dl^2)+1/12*D[0,0,1](u)(t,x,y,z)*(dt*rho(t,x,y,z)*dl+12*dt*rho(t,x,y,z)*omega_2^(-2)*dl-12*dt*rho(t,x,y,z)*omega_2^(-1)*dl)+1/12*D[1,1,1](u)(t,x,y,z)*(6*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*dl^3*omega_3^(-1)+12*dt^(-1)*rho(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-1)+18*dt^(-1)*c_s^2*rho(t,x,y,z)*omega_2^(-1)*dl^3+6*dt^(-1)*c_s^2*rho(t,x,y,z)*dl^3*omega_3^(-1)+18*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*omega_2^(-1)*dl^3-12*dt^(-1)*c_s^2*rho(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-1)+2*dt^(-1)*rho(t,x,y,z)*dl^3-5*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*dl^3-6*dt^(-1)*rho(t,x,y,z)*omega_2^(-1)*dl^3-12*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*omega_2^(-2)*dl^3-3*dt^(-1)*c_s^2*rho(t,x,y,z)*dl^3-12*dt^(-1)*c_s^2*rho(t,x,y,z)*omega_2^(-2)*dl^3-12*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-1)-6*dt^(-1)*rho(t,x,y,z)*dl^3*omega_3^(-1))+1/2*(dt^(-1)*u(t,x,y,z)*dl^2-2*dt^(-1)*u(t,x,y,z)*omega_2^(-1)*dl^2)*D[1](u)(t,x,y,z)*D[1](rho)(t,x,y,z)-1/12*D[1,1,1,1](u)(t,x,y,z)*(12*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*omega_2^(-1)*dl^4*omega_3^(-2)-dt^(-1)*c_s^2*u(t,x,y,z)*rho(t,x,y,z)*dl^4-8*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^4+12*dt^(-1)*c_s^2*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^4*omega_3^(-2)+6*dt^(-1)*c_s^2*u(t,x,y,z)*rho(t,x,y,z)*dl^4*omega_3^(-1)+24*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^4*omega_3^(-1)-24*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*omega_2^(-2)*dl^4+12*dt^(-1)*c_s^2*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-2)*dl^4*omega_3^(-1)+12*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*omega_2^(-2)*dl^4*omega_3^(-1)+12*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*omega_2^(-3)*dl^4-6*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^4*omega_3^(-1)-6*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*dl^4*omega_3^(-2)+20*dt^(-1)*c_s^2*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^4-42*dt^(-1)*c_s^2*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-2)*dl^4+6*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^4*omega_3^(-2)+6*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*dl^4*omega_3^(-1)+dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^4+24*dt^(-1)*c_s^2*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-3)*dl^4-2*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*dl^4-12*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-2)*dl^4*omega_3^(-1)-12*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^4*omega_3^(-2)-6*dt^(-1)*c_s^2*u(t,x,y,z)*rho(t,x,y,z)*dl^4*omega_3^(-2)-24*dt^(-1)*c_s^2*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^4*omega_3^(-1)+6*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-2)*dl^4+16*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*omega_2^(-1)*dl^4-24*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*omega_2^(-1)*dl^4*omega_3^(-1))-1/24*D[1,1,1,1](rho)(t,x,y,z)*(8*dt^(-1)*c_s^2*omega_2^(-1)*dl^4-12*dt^(-1)*c_s^2*u(t,x,y,z)^2*dl^4*omega_3^(-2)-24*dt^(-1)*c_s^2*omega_2^(-1)*dl^4*omega_3^(-1)+18*dt^(-1)*u(t,x,y,z)^4*dl^4*omega_3^(-1)+48*dt^(-1)*u(t,x,y,z)^4*omega_2^(-2)*dl^4*omega_3^(-1)+3*dt^(-1)*u(t,x,y,z)^2*dl^4-6*dt^(-1)*c_s^4*dl^4*omega_3^(-1)-48*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-1)*dl^4*omega_3^(-1)+24*dt^(-1)*u(t,x,y,z)^4*omega_2^(-1)*dl^4*omega_3^(-2)-24*dt^(-1)*u(t,x,y,z)^2*omega_2^(-1)*dl^4+96*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-3)*dl^4-dt^(-1)*c_s^2*dl^4-24*dt^(-1)*c_s^4*omega_2^(-1)*dl^4-18*dt^(-1)*u(t,x,y,z)^2*dl^4*omega_3^(-1)-24*dt^(-1)*c_s^4*omega_2^(-2)*dl^4*omega_3^(-1)+72*dt^(-1)*u(t,x,y,z)^2*omega_2^(-1)*dl^4*omega_3^(-1)+6*dt^(-1)*c_s^2*dl^4*omega_3^(-1)+24*dt^(-1)*u(t,x,y,z)^4*omega_2^(-1)*dl^4-156*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-2)*dl^4-3*dt^(-1)*u(t,x,y,z)^4*dl^4+24*dt^(-1)*c_s^4*omega_2^(-1)*dl^4*omega_3^(-1)-24*dt^(-1)*u(t,x,y,z)^4*omega_2^(-2)*dl^4+72*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-1)*dl^4+3*dt^(-1)*c_s^4*dl^4-48*dt^(-1)*u(t,x,y,z)^2*omega_2^(-2)*dl^4*omega_3^(-1)-24*dt^(-1)*u(t,x,y,z)^2*omega_2^(-1)*dl^4*omega_3^(-2)+48*dt^(-1)*c_s^4*omega_2^(-2)*dl^4+12*dt^(-1)*u(t,x,y,z)^2*dl^4*omega_3^(-2)+24*dt^(-1)*c_s^2*omega_2^(-2)*dl^4*omega_3^(-1)+24*dt^(-1)*u(t,x,y,z)^2*omega_2^(-2)*dl^4+24*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-1)*dl^4*omega_3^(-2)-72*dt^(-1)*u(t,x,y,z)^4*omega_2^(-1)*dl^4*omega_3^(-1)-12*dt^(-1)*c_s^2*omega_2^(-2)*dl^4+24*dt^(-1)*c_s^2*u(t,x,y,z)^2*omega_2^(-2)*dl^4*omega_3^(-1)+12*dt^(-1)*c_s^2*u(t,x,y,z)^2*dl^4*omega_3^(-1)-24*dt^(-1)*c_s^4*omega_2^(-3)*dl^4-12*dt^(-1)*u(t,x,y,z)^4*dl^4*omega_3^(-2)-6*dt^(-1)*c_s^2*u(t,x,y,z)^2*dl^4)+1/6*(u(t,x,y,z)*rho(t,x,y,z)*dl^2+12*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^2*omega_3^(-1)-6*u(t,x,y,z)*rho(t,x,y,z)*dl^2*omega_3^(-1)-6*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^2)*D[0,1,1](u)(t,x,y,z)+dt^(-1)*rho(t,x,y,z)*D[1](u)(t,x,y,z)*dl-1/2*D[0,0,0,1](u)(t,x,y,z)*(dt^2*rho(t,x,y,z)*omega_2^(-1)*dl-3*dt^2*rho(t,x,y,z)*omega_2^(-2)*dl+2*dt^2*rho(t,x,y,z)*omega_2^(-3)*dl)+1/2*(dt^(-1)*rho(t,x,y,z)*dl^2-2*dt^(-1)*rho(t,x,y,z)*omega_2^(-1)*dl^2)*D[1](u)(t,x,y,z)^2+dt^(-1)*u(t,x,y,z)*D[1](rho)(t,x,y,z)*dl+1/2*(rho(t,x,y,z)*dl-2*rho(t,x,y,z)*omega_2^(-1)*dl)*D[0,1](u)(t,x,y,z)+D[0](rho)(t,x,y,z)+1/2*(2*dt*u(t,x,y,z)*rho(t,x,y,z)*dl^2*omega_3^(-2)-dt*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-2)*dl^2-4*dt*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^2*omega_3^(-2)+2*dt*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-3)*dl^2-4*dt*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-2)*dl^2*omega_3^(-1)+8*dt*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^2*omega_3^(-1)-2*dt*u(t,x,y,z)*rho(t,x,y,z)*dl^2*omega_3^(-1)-dt*u(t,x,y,z)*rho(t,x,y,z)*omega_2^(-1)*dl^2)*D[0,0,1,1](u)(t,x,y,z)+1/6*(3*dt^(-1)*u(t,x,y,z)^3*dl^3*omega_3^(-1)-3*dt^(-1)*u(t,x,y,z)*omega_2^(-1)*dl^3+6*dt^(-1)*u(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-1)+dt^(-1)*u(t,x,y,z)*dl^3-12*dt^(-1)*c_s^2*u(t,x,y,z)*omega_2^(-2)*dl^3-6*dt^(-1)*c_s^2*u(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-1)+3*dt^(-1)*u(t,x,y,z)^3*omega_2^(-1)*dl^3-3*dt^(-1)*u(t,x,y,z)*dl^3*omega_3^(-1)-dt^(-1)*u(t,x,y,z)^3*dl^3+15*dt^(-1)*c_s^2*u(t,x,y,z)*omega_2^(-1)*dl^3+3*dt^(-1)*c_s^2*u(t,x,y,z)*dl^3*omega_3^(-1)-6*dt^(-1)*u(t,x,y,z)^3*omega_2^(-1)*dl^3*omega_3^(-1)-3*dt^(-1)*c_s^2*u(t,x,y,z)*dl^3)*D[1,1,1](rho)(t,x,y,z)+1/12*D[0,1,1,1](u)(t,x,y,z)*(15*u(t,x,y,z)^2*rho(t,x,y,z)*dl^3*omega_3^(-1)+36*rho(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-1)+48*u(t,x,y,z)^2*rho(t,x,y,z)*omega_2^(-2)*dl^3*omega_3^(-1)+6*rho(t,x,y,z)*dl^3*omega_3^(-2)+12*u(t,x,y,z)^2*rho(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-2)+25*c_s^2*rho(t,x,y,z)*omega_2^(-1)*dl^3+9*c_s^2*rho(t,x,y,z)*dl^3*omega_3^(-1)-36*c_s^2*rho(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-1)+12*rho(t,x,y,z)*omega_2^(-2)*dl^3+27*u(t,x,y,z)^2*rho(t,x,y,z)*omega_2^(-1)*dl^3+rho(t,x,y,z)*dl^3-3*u(t,x,y,z)^2*rho(t,x,y,z)*dl^3+24*c_s^2*rho(t,x,y,z)*omega_2^(-3)*dl^3-42*u(t,x,y,z)^2*rho(t,x,y,z)*omega_2^(-2)*dl^3-11*rho(t,x,y,z)*omega_2^(-1)*dl^3+12*c_s^2*rho(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-2)-6*c_s^2*rho(t,x,y,z)*dl^3*omega_3^(-2)+24*c_s^2*rho(t,x,y,z)*omega_2^(-2)*dl^3*omega_3^(-1)-2*c_s^2*rho(t,x,y,z)*dl^3-48*c_s^2*rho(t,x,y,z)*omega_2^(-2)*dl^3+12*u(t,x,y,z)^2*rho(t,x,y,z)*omega_2^(-3)*dl^3-60*u(t,x,y,z)^2*rho(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-1)-24*rho(t,x,y,z)*omega_2^(-2)*dl^3*omega_3^(-1)-12*rho(t,x,y,z)*omega_2^(-1)*dl^3*omega_3^(-2)-9*rho(t,x,y,z)*dl^3*omega_3^(-1)-6*u(t,x,y,z)^2*rho(t,x,y,z)*dl^3*omega_3^(-2))=0
List of all coefficients of each partial derivatives:
D[1](rho)
dt^(-1)*u*dl
D[1](u)
dt^(-1)*rho*dl
D[0](rho)
1
D[1,1](rho)
-dt^(-1)*c_s^2*omega_2^(-1)*dl^2+1/2*dt^(-1)*c_s^2*dl^2
D[1,1](u)
1/2*dt^(-1)*u*rho*dl^2-dt^(-1)*u*rho*omega_2^(-1)*dl^2
D[0,1](u)
1/2*rho*dl-rho*omega_2^(-1)*dl
D[1,1,1](rho)
1/2*dt^(-1)*u^3*dl^3*omega_3^(-1)-1/2*dt^(-1)*u*omega_2^(-1)*dl^3+dt^(-1)*u*omega_2^(-1)*dl^3*omega_3^(-1)+1/6*dt^(-1)*u*dl^3-2*dt^(-1)*c_s^2*u*omega_2^(-2)*dl^3-dt^(-1)*c_s^2*u*omega_2^(-1)*dl^3*omega_3^(-1)+1/2*dt^(-1)*u^3*omega_2^(-1)*dl^3-1/2*dt^(-1)*u*dl^3*omega_3^(-1)-1/6*dt^(-1)*u^3*dl^3+5/2*dt^(-1)*c_s^2*u*omega_2^(-1)*dl^3+1/2*dt^(-1)*c_s^2*u*dl^3*omega_3^(-1)-dt^(-1)*u^3*omega_2^(-1)*dl^3*omega_3^(-1)-1/2*dt^(-1)*c_s^2*u*dl^3
D[1,1,1](u)
1/2*dt^(-1)*u^2*rho*dl^3*omega_3^(-1)+dt^(-1)*rho*omega_2^(-1)*dl^3*omega_3^(-1)+3/2*dt^(-1)*c_s^2*rho*omega_2^(-1)*dl^3+1/2*dt^(-1)*c_s^2*rho*dl^3*omega_3^(-1)+3/2*dt^(-1)*u^2*rho*omega_2^(-1)*dl^3-dt^(-1)*c_s^2*rho*omega_2^(-1)*dl^3*omega_3^(-1)+1/6*dt^(-1)*rho*dl^3-5/12*dt^(-1)*u^2*rho*dl^3-1/2*dt^(-1)*rho*omega_2^(-1)*dl^3-dt^(-1)*u^2*rho*omega_2^(-2)*dl^3-1/4*dt^(-1)*c_s^2*rho*dl^3-dt^(-1)*c_s^2*rho*omega_2^(-2)*dl^3-dt^(-1)*u^2*rho*omega_2^(-1)*dl^3*omega_3^(-1)-1/2*dt^(-1)*rho*dl^3*omega_3^(-1)
D[0,1,1](u)
1/6*u*rho*dl^2+2*u*rho*omega_2^(-1)*dl^2*omega_3^(-1)-u*rho*dl^2*omega_3^(-1)-u*rho*omega_2^(-1)*dl^2
D[0,0,1](u)
1/12*dt*rho*dl+dt*rho*omega_2^(-2)*dl-dt*rho*omega_2^(-1)*dl
D[1,1,1,1](rho)
-1/3*dt^(-1)*c_s^2*omega_2^(-1)*dl^4+1/2*dt^(-1)*c_s^2*u^2*dl^4*omega_3^(-2)+dt^(-1)*c_s^2*omega_2^(-1)*dl^4*omega_3^(-1)-3/4*dt^(-1)*u^4*dl^4*omega_3^(-1)-2*dt^(-1)*u^4*omega_2^(-2)*dl^4*omega_3^(-1)-1/8*dt^(-1)*u^2*dl^4+1/4*dt^(-1)*c_s^4*dl^4*omega_3^(-1)+2*dt^(-1)*c_s^2*u^2*omega_2^(-1)*dl^4*omega_3^(-1)-dt^(-1)*u^4*omega_2^(-1)*dl^4*omega_3^(-2)+dt^(-1)*u^2*omega_2^(-1)*dl^4-4*dt^(-1)*c_s^2*u^2*omega_2^(-3)*dl^4+1/24*dt^(-1)*c_s^2*dl^4+dt^(-1)*c_s^4*omega_2^(-1)*dl^4+3/4*dt^(-1)*u^2*dl^4*omega_3^(-1)+dt^(-1)*c_s^4*omega_2^(-2)*dl^4*omega_3^(-1)-3*dt^(-1)*u^2*omega_2^(-1)*dl^4*omega_3^(-1)-1/4*dt^(-1)*c_s^2*dl^4*omega_3^(-1)-dt^(-1)*u^4*omega_2^(-1)*dl^4+13/2*dt^(-1)*c_s^2*u^2*omega_2^(-2)*dl^4+1/8*dt^(-1)*u^4*dl^4-dt^(-1)*c_s^4*omega_2^(-1)*dl^4*omega_3^(-1)+dt^(-1)*u^4*omega_2^(-2)*dl^4-3*dt^(-1)*c_s^2*u^2*omega_2^(-1)*dl^4-1/8*dt^(-1)*c_s^4*dl^4+2*dt^(-1)*u^2*omega_2^(-2)*dl^4*omega_3^(-1)+dt^(-1)*u^2*omega_2^(-1)*dl^4*omega_3^(-2)-2*dt^(-1)*c_s^4*omega_2^(-2)*dl^4-1/2*dt^(-1)*u^2*dl^4*omega_3^(-2)-dt^(-1)*c_s^2*omega_2^(-2)*dl^4*omega_3^(-1)-dt^(-1)*u^2*omega_2^(-2)*dl^4-dt^(-1)*c_s^2*u^2*omega_2^(-1)*dl^4*omega_3^(-2)+3*dt^(-1)*u^4*omega_2^(-1)*dl^4*omega_3^(-1)+1/2*dt^(-1)*c_s^2*omega_2^(-2)*dl^4-dt^(-1)*c_s^2*u^2*omega_2^(-2)*dl^4*omega_3^(-1)-1/2*dt^(-1)*c_s^2*u^2*dl^4*omega_3^(-1)+dt^(-1)*c_s^4*omega_2^(-3)*dl^4+1/2*dt^(-1)*u^4*dl^4*omega_3^(-2)+1/4*dt^(-1)*c_s^2*u^2*dl^4
D[1,1,1,1](u)
-dt^(-1)*u^3*rho*omega_2^(-1)*dl^4*omega_3^(-2)+1/12*dt^(-1)*c_s^2*u*rho*dl^4+2/3*dt^(-1)*u*rho*omega_2^(-1)*dl^4-dt^(-1)*c_s^2*u*rho*omega_2^(-1)*dl^4*omega_3^(-2)-1/2*dt^(-1)*c_s^2*u*rho*dl^4*omega_3^(-1)-2*dt^(-1)*u*rho*omega_2^(-1)*dl^4*omega_3^(-1)+2*dt^(-1)*u^3*rho*omega_2^(-2)*dl^4-dt^(-1)*c_s^2*u*rho*omega_2^(-2)*dl^4*omega_3^(-1)-dt^(-1)*u^3*rho*omega_2^(-2)*dl^4*omega_3^(-1)-dt^(-1)*u^3*rho*omega_2^(-3)*dl^4+1/2*dt^(-1)*u*rho*dl^4*omega_3^(-1)+1/2*dt^(-1)*u^3*rho*dl^4*omega_3^(-2)-5/3*dt^(-1)*c_s^2*u*rho*omega_2^(-1)*dl^4+7/2*dt^(-1)*c_s^2*u*rho*omega_2^(-2)*dl^4-1/2*dt^(-1)*u*rho*dl^4*omega_3^(-2)-1/2*dt^(-1)*u^3*rho*dl^4*omega_3^(-1)-1/12*dt^(-1)*u*rho*dl^4-2*dt^(-1)*c_s^2*u*rho*omega_2^(-3)*dl^4+1/6*dt^(-1)*u^3*rho*dl^4+dt^(-1)*u*rho*omega_2^(-2)*dl^4*omega_3^(-1)+dt^(-1)*u*rho*omega_2^(-1)*dl^4*omega_3^(-2)+1/2*dt^(-1)*c_s^2*u*rho*dl^4*omega_3^(-2)+2*dt^(-1)*c_s^2*u*rho*omega_2^(-1)*dl^4*omega_3^(-1)-1/2*dt^(-1)*u*rho*omega_2^(-2)*dl^4-4/3*dt^(-1)*u^3*rho*omega_2^(-1)*dl^4+2*dt^(-1)*u^3*rho*omega_2^(-1)*dl^4*omega_3^(-1)
D[0,1,1,1](u)
5/4*u^2*rho*dl^3*omega_3^(-1)+3*rho*omega_2^(-1)*dl^3*omega_3^(-1)+4*u^2*rho*omega_2^(-2)*dl^3*omega_3^(-1)+1/2*rho*dl^3*omega_3^(-2)+u^2*rho*omega_2^(-1)*dl^3*omega_3^(-2)+25/12*c_s^2*rho*omega_2^(-1)*dl^3+3/4*c_s^2*rho*dl^3*omega_3^(-1)-3*c_s^2*rho*omega_2^(-1)*dl^3*omega_3^(-1)+rho*omega_2^(-2)*dl^3+9/4*u^2*rho*omega_2^(-1)*dl^3+1/12*rho*dl^3-1/4*u^2*rho*dl^3+2*c_s^2*rho*omega_2^(-3)*dl^3-7/2*u^2*rho*omega_2^(-2)*dl^3-11/12*rho*omega_2^(-1)*dl^3+c_s^2*rho*omega_2^(-1)*dl^3*omega_3^(-2)-1/2*c_s^2*rho*dl^3*omega_3^(-2)+2*c_s^2*rho*omega_2^(-2)*dl^3*omega_3^(-1)-1/6*c_s^2*rho*dl^3-4*c_s^2*rho*omega_2^(-2)*dl^3+u^2*rho*omega_2^(-3)*dl^3-5*u^2*rho*omega_2^(-1)*dl^3*omega_3^(-1)-2*rho*omega_2^(-2)*dl^3*omega_3^(-1)-rho*omega_2^(-1)*dl^3*omega_3^(-2)-3/4*rho*dl^3*omega_3^(-1)-1/2*u^2*rho*dl^3*omega_3^(-2)
D[0,0,1,1](u)
dt*u*rho*dl^2*omega_3^(-2)-1/2*dt*u*rho*omega_2^(-2)*dl^2-2*dt*u*rho*omega_2^(-1)*dl^2*omega_3^(-2)+dt*u*rho*omega_2^(-3)*dl^2-2*dt*u*rho*omega_2^(-2)*dl^2*omega_3^(-1)+4*dt*u*rho*omega_2^(-1)*dl^2*omega_3^(-1)-dt*u*rho*dl^2*omega_3^(-1)-1/2*dt*u*rho*omega_2^(-1)*dl^2
D[0,0,0,1](u)
-1/2*dt^2*rho*omega_2^(-1)*dl+3/2*dt^2*rho*omega_2^(-2)*dl-dt^2*rho*omega_2^(-3)*dl
D[1](rho) * D[1](u)
1/2*dt^(-1)*u*dl^2-dt^(-1)*u*omega_2^(-1)*dl^2
D[1](u) * D[1](u)
1/2*dt^(-1)*rho*dl^2-dt^(-1)*rho*omega_2^(-1)*dl^2
D[1](rho) * D[0](u)
-omega_2^(-1)*dl+1/2*dl
supp_d1q3_ade_txt/output_d1q3_ade_srt_symbolic_pde_00.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
-1/6*(u(t,x,y,z)^3*dl^3*dt^(-1)-18*omega^(-1)*u(t,x,y,z)*dl^3*dt^(-1)*c_s^2-6*omega^(-1)*u(t,x,y,z)^3*dl^3*dt^(-1)+18*omega^(-2)*u(t,x,y,z)*dl^3*dt^(-1)*c_s^2+6*omega^(-1)*u(t,x,y,z)*dl^3*dt^(-1)+3*u(t,x,y,z)*dl^3*dt^(-1)*c_s^2-u(t,x,y,z)*dl^3*dt^(-1)+6*omega^(-2)*u(t,x,y,z)^3*dl^3*dt^(-1)-6*omega^(-2)*u(t,x,y,z)*dl^3*dt^(-1))*D[1,1,1](rho)(t,x,y,z)+1/2*D[1,1](u)(t,x,y,z)*(rho(t,x,y,z)*u(t,x,y,z)*dl^2*dt^(-1)-2*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^2*dt^(-1))-1/12*(5*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3*dt^(-1)+24*omega^(-2)*rho(t,x,y,z)*dl^3*dt^(-1)*c_s^2-24*omega^(-1)*rho(t,x,y,z)*dl^3*dt^(-1)*c_s^2-24*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3*dt^(-1)-12*omega^(-2)*rho(t,x,y,z)*dl^3*dt^(-1)+3*rho(t,x,y,z)*dl^3*dt^(-1)*c_s^2+24*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3*dt^(-1)+12*omega^(-1)*rho(t,x,y,z)*dl^3*dt^(-1)-2*rho(t,x,y,z)*dl^3*dt^(-1))*D[1,1,1](u)(t,x,y,z)+1/6*(12*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)*dl^2+rho(t,x,y,z)*u(t,x,y,z)*dl^2-12*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^2)*D[0,1,1](u)(t,x,y,z)-1/2*(2*omega^(-1)*rho(t,x,y,z)*dl^2*dt^(-1)-rho(t,x,y,z)*dl^2*dt^(-1))*D[1](u)(t,x,y,z)^2+1/2*D[1](rho)(t,x,y,z)*D[0](u)(t,x,y,z)*(dl-2*omega^(-1)*dl)-3/2*(omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^2*dt-3*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)*dl^2*dt+2*omega^(-3)*rho(t,x,y,z)*u(t,x,y,z)*dl^2*dt)*D[0,0,1,1](u)(t,x,y,z)-1/24*(14*omega^(-1)*dl^4*dt^(-1)*c_s^2-3*u(t,x,y,z)^4*dl^4*dt^(-1)+42*omega^(-1)*u(t,x,y,z)^4*dl^4*dt^(-1)-dl^4*dt^(-1)*c_s^2-48*omega^(-3)*dl^4*dt^(-1)*c_s^4-6*u(t,x,y,z)^2*dl^4*dt^(-1)*c_s^2+72*omega^(-2)*dl^4*dt^(-1)*c_s^4+3*u(t,x,y,z)^2*dl^4*dt^(-1)-216*omega^(-2)*u(t,x,y,z)^2*dl^4*dt^(-1)*c_s^2-42*omega^(-1)*u(t,x,y,z)^2*dl^4*dt^(-1)+84*omega^(-1)*u(t,x,y,z)^2*dl^4*dt^(-1)*c_s^2+144*omega^(-3)*u(t,x,y,z)^2*dl^4*dt^(-1)*c_s^2-72*omega^(-3)*u(t,x,y,z)^2*dl^4*dt^(-1)-36*omega^(-2)*dl^4*dt^(-1)*c_s^2-108*omega^(-2)*u(t,x,y,z)^4*dl^4*dt^(-1)+72*omega^(-3)*u(t,x,y,z)^4*dl^4*dt^(-1)-30*omega^(-1)*dl^4*dt^(-1)*c_s^4+3*dl^4*dt^(-1)*c_s^4+108*omega^(-2)*u(t,x,y,z)^2*dl^4*dt^(-1)+24*omega^(-3)*dl^4*dt^(-1)*c_s^2)*D[1,1,1,1](rho)(t,x,y,z)+1/12*D[0,1,1,1](u)(t,x,y,z)*(60*omega^(-3)*rho(t,x,y,z)*dl^3*c_s^2-20*omega^(-1)*rho(t,x,y,z)*dl^3-3*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3-36*omega^(-3)*rho(t,x,y,z)*dl^3+42*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3-90*omega^(-2)*rho(t,x,y,z)*dl^3*c_s^2+72*omega^(-3)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3+rho(t,x,y,z)*dl^3-2*rho(t,x,y,z)*dl^3*c_s^2+54*omega^(-2)*rho(t,x,y,z)*dl^3+34*omega^(-1)*rho(t,x,y,z)*dl^3*c_s^2-108*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3)+D[0](rho)(t,x,y,z)+rho(t,x,y,z)*dl*D[1](u)(t,x,y,z)*dt^(-1)-1/12*(22*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1)+rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)-54*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1)-72*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*c_s^2+36*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)-2*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1)+26*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*c_s^2-14*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)+48*omega^(-3)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*c_s^2-24*omega^(-3)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)+36*omega^(-3)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1)-rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*c_s^2)*D[1,1,1,1](u)(t,x,y,z)-1/2*(2*omega^(-3)*rho(t,x,y,z)*dl*dt^2-3*omega^(-2)*rho(t,x,y,z)*dl*dt^2+omega^(-1)*rho(t,x,y,z)*dl*dt^2)*D[0,0,0,1](u)(t,x,y,z)-1/2*(2*omega^(-1)*rho(t,x,y,z)*dl-rho(t,x,y,z)*dl)*D[0,1](u)(t,x,y,z)+u(t,x,y,z)*dl*D[1](rho)(t,x,y,z)*dt^(-1)+1/12*(12*omega^(-2)*rho(t,x,y,z)*dl*dt+rho(t,x,y,z)*dl*dt-12*omega^(-1)*rho(t,x,y,z)*dl*dt)*D[0,0,1](u)(t,x,y,z)-1/2*(2*omega^(-1)*u(t,x,y,z)*dl^2*dt^(-1)-u(t,x,y,z)*dl^2*dt^(-1))*D[1](rho)(t,x,y,z)*D[1](u)(t,x,y,z)-1/2*D[1,1](rho)(t,x,y,z)*(2*omega^(-1)*dl^2*dt^(-1)*c_s^2-dl^2*dt^(-1)*c_s^2)=0
List of all coefficients of each partial derivatives:
D[1](rho)
u*dl*dt^(-1)
D[1](u)
rho*dl*dt^(-1)
D[0](rho)
1
D[1,1](rho)
-omega^(-1)*dl^2*dt^(-1)*c_s^2+1/2*dl^2*dt^(-1)*c_s^2
D[1,1](u)
1/2*rho*u*dl^2*dt^(-1)-omega^(-1)*rho*u*dl^2*dt^(-1)
D[0,1](u)
-omega^(-1)*rho*dl+1/2*rho*dl
D[1,1,1](rho)
-1/6*u^3*dl^3*dt^(-1)+3*omega^(-1)*u*dl^3*dt^(-1)*c_s^2+omega^(-1)*u^3*dl^3*dt^(-1)-3*omega^(-2)*u*dl^3*dt^(-1)*c_s^2-omega^(-1)*u*dl^3*dt^(-1)-1/2*u*dl^3*dt^(-1)*c_s^2+1/6*u*dl^3*dt^(-1)-omega^(-2)*u^3*dl^3*dt^(-1)+omega^(-2)*u*dl^3*dt^(-1)
D[1,1,1](u)
-5/12*rho*u^2*dl^3*dt^(-1)-2*omega^(-2)*rho*dl^3*dt^(-1)*c_s^2+2*omega^(-1)*rho*dl^3*dt^(-1)*c_s^2+2*omega^(-1)*rho*u^2*dl^3*dt^(-1)+omega^(-2)*rho*dl^3*dt^(-1)-1/4*rho*dl^3*dt^(-1)*c_s^2-2*omega^(-2)*rho*u^2*dl^3*dt^(-1)-omega^(-1)*rho*dl^3*dt^(-1)+1/6*rho*dl^3*dt^(-1)
D[0,1,1](u)
2*omega^(-2)*rho*u*dl^2+1/6*rho*u*dl^2-2*omega^(-1)*rho*u*dl^2
D[0,0,1](u)
omega^(-2)*rho*dl*dt+1/12*rho*dl*dt-omega^(-1)*rho*dl*dt
D[1,1,1,1](rho)
-7/12*omega^(-1)*dl^4*dt^(-1)*c_s^2+1/8*u^4*dl^4*dt^(-1)-7/4*omega^(-1)*u^4*dl^4*dt^(-1)+1/24*dl^4*dt^(-1)*c_s^2+2*omega^(-3)*dl^4*dt^(-1)*c_s^4+1/4*u^2*dl^4*dt^(-1)*c_s^2-3*omega^(-2)*dl^4*dt^(-1)*c_s^4-1/8*u^2*dl^4*dt^(-1)+9*omega^(-2)*u^2*dl^4*dt^(-1)*c_s^2+7/4*omega^(-1)*u^2*dl^4*dt^(-1)-7/2*omega^(-1)*u^2*dl^4*dt^(-1)*c_s^2-6*omega^(-3)*u^2*dl^4*dt^(-1)*c_s^2+3*omega^(-3)*u^2*dl^4*dt^(-1)+3/2*omega^(-2)*dl^4*dt^(-1)*c_s^2+9/2*omega^(-2)*u^4*dl^4*dt^(-1)-3*omega^(-3)*u^4*dl^4*dt^(-1)+5/4*omega^(-1)*dl^4*dt^(-1)*c_s^4-1/8*dl^4*dt^(-1)*c_s^4-9/2*omega^(-2)*u^2*dl^4*dt^(-1)-omega^(-3)*dl^4*dt^(-1)*c_s^2
D[1,1,1,1](u)
-11/6*omega^(-1)*rho*u^3*dl^4*dt^(-1)-1/12*rho*u*dl^4*dt^(-1)+9/2*omega^(-2)*rho*u^3*dl^4*dt^(-1)+6*omega^(-2)*rho*u*dl^4*dt^(-1)*c_s^2-3*omega^(-2)*rho*u*dl^4*dt^(-1)+1/6*rho*u^3*dl^4*dt^(-1)-13/6*omega^(-1)*rho*u*dl^4*dt^(-1)*c_s^2+7/6*omega^(-1)*rho*u*dl^4*dt^(-1)-4*omega^(-3)*rho*u*dl^4*dt^(-1)*c_s^2+2*omega^(-3)*rho*u*dl^4*dt^(-1)-3*omega^(-3)*rho*u^3*dl^4*dt^(-1)+1/12*rho*u*dl^4*dt^(-1)*c_s^2
D[0,1,1,1](u)
5*omega^(-3)*rho*dl^3*c_s^2-5/3*omega^(-1)*rho*dl^3-1/4*rho*u^2*dl^3-3*omega^(-3)*rho*dl^3+7/2*omega^(-1)*rho*u^2*dl^3-15/2*omega^(-2)*rho*dl^3*c_s^2+6*omega^(-3)*rho*u^2*dl^3+1/12*rho*dl^3-1/6*rho*dl^3*c_s^2+9/2*omega^(-2)*rho*dl^3+17/6*omega^(-1)*rho*dl^3*c_s^2-9*omega^(-2)*rho*u^2*dl^3
D[0,0,1,1](u)
-3/2*omega^(-1)*rho*u*dl^2*dt+9/2*omega^(-2)*rho*u*dl^2*dt-3*omega^(-3)*rho*u*dl^2*dt
D[0,0,0,1](u)
-omega^(-3)*rho*dl*dt^2+3/2*omega^(-2)*rho*dl*dt^2-1/2*omega^(-1)*rho*dl*dt^2
D[1](rho) * D[1](u)
-omega^(-1)*u*dl^2*dt^(-1)+1/2*u*dl^2*dt^(-1)
D[1](u) * D[1](u)
-omega^(-1)*rho*dl^2*dt^(-1)+1/2*rho*dl^2*dt^(-1)
D[1](rho) * D[0](u)
1/2*dl-omega^(-1)*dl
supp_d1q3_nse_txt/output_d1q3_nse_clbm1_symbolic_pde_00.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
dl*D[1](u)(t,x,y,z)*dt^(-1)*rho(t,x,y,z)+1/12*D[1,1,1,1](u)(t,x,y,z)*(10*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)-5*dl^4*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)-3*dl^4*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*cs^2+2*dl^4*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)-4*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)+6*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*cs^2)+dl*D[1](rho)(t,x,y,z)*dt^(-1)*u(t,x,y,z)+1/12*(dl^3*dt^(-1)*rho(t,x,y,z)*cs^2-dl^3*dt^(-1)*rho(t,x,y,z)+3*dl^3*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z))*D[1,1,1](u)(t,x,y,z)+D[0](rho)(t,x,y,z)-1/24*(2*dl^4*omega_3^(-1)*dt^(-1)*cs^2+3*dl^4*dt^(-1)*u(t,x,y,z)^4+12*dl^4*dt^(-1)*u(t,x,y,z)^2*cs^2+dl^4*dt^(-1)*cs^4+6*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2-24*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*cs^2-dl^4*dt^(-1)*cs^2-6*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^4-2*dl^4*omega_3^(-1)*dt^(-1)*cs^4-3*dl^4*dt^(-1)*u(t,x,y,z)^2)*D[1,1,1,1](rho)(t,x,y,z)+1/12*(dl^3*dt^(-1)*u(t,x,y,z)^3+3*dl^3*dt^(-1)*u(t,x,y,z)*cs^2-dl^3*dt^(-1)*u(t,x,y,z))*D[1,1,1](rho)(t,x,y,z)=0
List of all coefficients of each partial derivatives:
D[1](rho)
dl*dt^(-1)*u
D[1](u)
dl*dt^(-1)*rho
D[0](rho)
1
D[1,1,1](rho)
1/12*dl^3*dt^(-1)*u^3+1/4*dl^3*dt^(-1)*u*cs^2-1/12*dl^3*dt^(-1)*u
D[1,1,1](u)
1/12*dl^3*dt^(-1)*rho*cs^2-1/12*dl^3*dt^(-1)*rho+1/4*dl^3*dt^(-1)*u^2*rho
D[1,1,1,1](rho)
-1/12*dl^4*omega_3^(-1)*dt^(-1)*cs^2-1/8*dl^4*dt^(-1)*u^4-1/2*dl^4*dt^(-1)*u^2*cs^2-1/24*dl^4*dt^(-1)*cs^4-1/4*dl^4*omega_3^(-1)*dt^(-1)*u^2+dl^4*omega_3^(-1)*dt^(-1)*u^2*cs^2+1/24*dl^4*dt^(-1)*cs^2+1/4*dl^4*omega_3^(-1)*dt^(-1)*u^4+1/12*dl^4*omega_3^(-1)*dt^(-1)*cs^4+1/8*dl^4*dt^(-1)*u^2
D[1,1,1,1](u)
5/6*dl^4*omega_3^(-1)*dt^(-1)*u^3*rho-5/12*dl^4*dt^(-1)*u^3*rho-1/4*dl^4*dt^(-1)*u*rho*cs^2+1/6*dl^4*dt^(-1)*u*rho-1/3*dl^4*omega_3^(-1)*dt^(-1)*u*rho+1/2*dl^4*omega_3^(-1)*dt^(-1)*u*rho*cs^2
supp_d1q3_nse_txt/output_d1q3_nse_clbm1_symbolic_pde_01.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
1/12*(24*dl^4*omega_3^(-3)*dt^(-1)*cs^4*rho(t,x,y,z)+504*dl^4*omega_3^(-3)*dt^(-1)*u(t,x,y,z)^4*rho(t,x,y,z)+8*dl^4*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)+12*dl^4*omega_3^(-3)*dt^(-1)*rho(t,x,y,z)-154*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)-22*dl^4*omega_3^(-1)*dt^(-1)*cs^2*rho(t,x,y,z)-36*dl^4*omega_3^(-2)*dt^(-1)*cs^4*rho(t,x,y,z)+432*dl^4*omega_3^(-3)*dt^(-1)*cs^2*u(t,x,y,z)^2*rho(t,x,y,z)+2*dl^4*dt^(-1)*cs^2*rho(t,x,y,z)-756*dl^4*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^4*rho(t,x,y,z)+14*dl^4*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)+252*dl^4*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)^2*rho(t,x,y,z)-dl^4*dt^(-1)*rho(t,x,y,z)-36*dl^4*omega_3^(-3)*dt^(-1)*cs^2*rho(t,x,y,z)-252*dl^4*omega_3^(-3)*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)-648*dl^4*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)^2*rho(t,x,y,z)+54*dl^4*omega_3^(-2)*dt^(-1)*cs^2*rho(t,x,y,z)-dl^4*dt^(-1)*cs^4*rho(t,x,y,z)+378*dl^4*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)-29*dl^4*dt^(-1)*u(t,x,y,z)^4*rho(t,x,y,z)-18*dl^4*dt^(-1)*cs^2*u(t,x,y,z)^2*rho(t,x,y,z)+310*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^4*rho(t,x,y,z)-18*dl^4*omega_3^(-2)*dt^(-1)*rho(t,x,y,z)+14*dl^4*omega_3^(-1)*dt^(-1)*cs^4*rho(t,x,y,z))*D[1,1,1,1](u)(t,x,y,z)-(2*dl^2*omega_3^(-1)*dt^(-1)+3*dl^2*dt^(-1)*u(t,x,y,z)^2+2*dl^2*dt^(-1)*cs^2-dl^2*dt^(-1)-6*dl^2*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2-4*dl^2*omega_3^(-1)*dt^(-1)*cs^2)*D[1](u)(t,x,y,z)*D[1](rho)(t,x,y,z)+D[0](u)(t,x,y,z)*rho(t,x,y,z)+2*dl*D[1](u)(t,x,y,z)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)+D[1](rho)(t,x,y,z)*(dl*dt^(-1)*cs^2+dl*dt^(-1)*u(t,x,y,z)^2)+D[0](rho)(t,x,y,z)*u(t,x,y,z)-1/12*(34*dl^4*dt^(-1)*cs^2*u(t,x,y,z)^3-8*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)-404*dl^4*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)^3-144*dl^4*omega_3^(-3)*dt^(-1)*cs^4*u(t,x,y,z)+9*dl^4*dt^(-1)*u(t,x,y,z)^5+156*dl^4*omega_3^(-3)*dt^(-1)*u(t,x,y,z)^3+98*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3+216*dl^4*omega_3^(-2)*dt^(-1)*cs^4*u(t,x,y,z)-6*dl^4*dt^(-1)*cs^2*u(t,x,y,z)+216*dl^4*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^5-12*dl^4*omega_3^(-3)*dt^(-1)*u(t,x,y,z)+78*dl^4*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)+dl^4*dt^(-1)*u(t,x,y,z)+132*dl^4*omega_3^(-3)*dt^(-1)*cs^2*u(t,x,y,z)-234*dl^4*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^3-90*dl^4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^5+1008*dl^4*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)^3+18*dl^4*omega_3^(-2)*dt^(-1)*u(t,x,y,z)-672*dl^4*omega_3^(-3)*dt^(-1)*cs^2*u(t,x,y,z)^3-144*dl^4*omega_3^(-3)*dt^(-1)*u(t,x,y,z)^5-10*dl^4*dt^(-1)*u(t,x,y,z)^3-82*dl^4*omega_3^(-1)*dt^(-1)*cs^4*u(t,x,y,z)-198*dl^4*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)+5*dl^4*dt^(-1)*cs^4*u(t,x,y,z))*D[1,1,1,1](rho)(t,x,y,z)+1/6*(60*dl^3*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)+24*dl^3*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)-4*dl^3*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)+36*dl^3*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)*rho(t,x,y,z)+5*dl^3*dt^(-1)*cs^2*u(t,x,y,z)*rho(t,x,y,z)+11*dl^3*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)-60*dl^3*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)-36*dl^3*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)*rho(t,x,y,z)-24*dl^3*omega_3^(-2)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z))*D[1,1,1](u)(t,x,y,z)-3*D[1](u)(t,x,y,z)^2*(dl^2*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)-2*dl^2*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z))+1/2*D[1,1](rho)(t,x,y,z)*(6*dl^2*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)-2*dl^2*omega_3^(-1)*dt^(-1)*u(t,x,y,z)-dl^2*dt^(-1)*u(t,x,y,z)^3+dl^2*dt^(-1)*u(t,x,y,z)-3*dl^2*dt^(-1)*cs^2*u(t,x,y,z)+2*dl^2*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3)-1/12*D[1,1,1](rho)(t,x,y,z)*(7*dl^3*dt^(-1)*u(t,x,y,z)^2+dl^3*dt^(-1)*cs^2+36*dl^3*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^2+12*dl^3*omega_3^(-2)*dt^(-1)*cs^2+12*dl^3*omega_3^(-1)*dt^(-1)*cs^4+36*dl^3*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^4-144*dl^3*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)^2-12*dl^3*omega_3^(-1)*dt^(-1)*cs^2-36*dl^3*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2-36*dl^3*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^4-12*dl^3*omega_3^(-2)*dt^(-1)*cs^4+144*dl^3*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)^2-7*dl^3*dt^(-1)*u(t,x,y,z)^4-24*dl^3*dt^(-1)*cs^2*u(t,x,y,z)^2-dl^3*dt^(-1)*cs^4)+1/2*(2*dl^2*omega_3^(-1)*dt^(-1)*cs^2*rho(t,x,y,z)+6*dl^2*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)-2*dl^2*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)-dl^2*dt^(-1)*cs^2*rho(t,x,y,z)+dl^2*dt^(-1)*rho(t,x,y,z)-3*dl^2*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z))*D[1,1](u)(t,x,y,z)=0
List of all coefficients of each partial derivatives:
D[1](rho)
dl*dt^(-1)*cs^2+dl*dt^(-1)*u^2
D[1](u)
2*dl*dt^(-1)*u*rho
D[0](rho)
u
D[0](u)
rho
D[1,1](rho)
3*dl^2*omega_3^(-1)*dt^(-1)*cs^2*u-dl^2*omega_3^(-1)*dt^(-1)*u-1/2*dl^2*dt^(-1)*u^3+1/2*dl^2*dt^(-1)*u-3/2*dl^2*dt^(-1)*cs^2*u+dl^2*omega_3^(-1)*dt^(-1)*u^3
D[1,1](u)
dl^2*omega_3^(-1)*dt^(-1)*cs^2*rho+3*dl^2*omega_3^(-1)*dt^(-1)*u^2*rho-dl^2*omega_3^(-1)*dt^(-1)*rho-1/2*dl^2*dt^(-1)*cs^2*rho+1/2*dl^2*dt^(-1)*rho-3/2*dl^2*dt^(-1)*u^2*rho
D[1,1,1](rho)
-7/12*dl^3*dt^(-1)*u^2-1/12*dl^3*dt^(-1)*cs^2-3*dl^3*omega_3^(-2)*dt^(-1)*u^2-dl^3*omega_3^(-2)*dt^(-1)*cs^2-dl^3*omega_3^(-1)*dt^(-1)*cs^4-3*dl^3*omega_3^(-1)*dt^(-1)*u^4+12*dl^3*omega_3^(-2)*dt^(-1)*cs^2*u^2+dl^3*omega_3^(-1)*dt^(-1)*cs^2+3*dl^3*omega_3^(-1)*dt^(-1)*u^2+3*dl^3*omega_3^(-2)*dt^(-1)*u^4+dl^3*omega_3^(-2)*dt^(-1)*cs^4-12*dl^3*omega_3^(-1)*dt^(-1)*cs^2*u^2+7/12*dl^3*dt^(-1)*u^4+2*dl^3*dt^(-1)*cs^2*u^2+1/12*dl^3*dt^(-1)*cs^4
D[1,1,1](u)
10*dl^3*omega_3^(-2)*dt^(-1)*u^3*rho+4*dl^3*omega_3^(-1)*dt^(-1)*u*rho-2/3*dl^3*dt^(-1)*u*rho+6*dl^3*omega_3^(-2)*dt^(-1)*cs^2*u*rho+5/6*dl^3*dt^(-1)*cs^2*u*rho+11/6*dl^3*dt^(-1)*u^3*rho-10*dl^3*omega_3^(-1)*dt^(-1)*u^3*rho-6*dl^3*omega_3^(-1)*dt^(-1)*cs^2*u*rho-4*dl^3*omega_3^(-2)*dt^(-1)*u*rho
D[1,1,1,1](rho)
-17/6*dl^4*dt^(-1)*cs^2*u^3+2/3*dl^4*omega_3^(-1)*dt^(-1)*u+101/3*dl^4*omega_3^(-1)*dt^(-1)*cs^2*u^3+12*dl^4*omega_3^(-3)*dt^(-1)*cs^4*u-3/4*dl^4*dt^(-1)*u^5-13*dl^4*omega_3^(-3)*dt^(-1)*u^3-49/6*dl^4*omega_3^(-1)*dt^(-1)*u^3-18*dl^4*omega_3^(-2)*dt^(-1)*cs^4*u+1/2*dl^4*dt^(-1)*cs^2*u-18*dl^4*omega_3^(-2)*dt^(-1)*u^5+dl^4*omega_3^(-3)*dt^(-1)*u-13/2*dl^4*omega_3^(-1)*dt^(-1)*cs^2*u-1/12*dl^4*dt^(-1)*u-11*dl^4*omega_3^(-3)*dt^(-1)*cs^2*u+39/2*dl^4*omega_3^(-2)*dt^(-1)*u^3+15/2*dl^4*omega_3^(-1)*dt^(-1)*u^5-84*dl^4*omega_3^(-2)*dt^(-1)*cs^2*u^3-3/2*dl^4*omega_3^(-2)*dt^(-1)*u+56*dl^4*omega_3^(-3)*dt^(-1)*cs^2*u^3+12*dl^4*omega_3^(-3)*dt^(-1)*u^5+5/6*dl^4*dt^(-1)*u^3+41/6*dl^4*omega_3^(-1)*dt^(-1)*cs^4*u+33/2*dl^4*omega_3^(-2)*dt^(-1)*cs^2*u-5/12*dl^4*dt^(-1)*cs^4*u
D[1,1,1,1](u)
2*dl^4*omega_3^(-3)*dt^(-1)*cs^4*rho+42*dl^4*omega_3^(-3)*dt^(-1)*u^4*rho+2/3*dl^4*omega_3^(-1)*dt^(-1)*rho+dl^4*omega_3^(-3)*dt^(-1)*rho-77/6*dl^4*omega_3^(-1)*dt^(-1)*u^2*rho-11/6*dl^4*omega_3^(-1)*dt^(-1)*cs^2*rho-3*dl^4*omega_3^(-2)*dt^(-1)*cs^4*rho+36*dl^4*omega_3^(-3)*dt^(-1)*cs^2*u^2*rho+1/6*dl^4*dt^(-1)*cs^2*rho-63*dl^4*omega_3^(-2)*dt^(-1)*u^4*rho+7/6*dl^4*dt^(-1)*u^2*rho+21*dl^4*omega_3^(-1)*dt^(-1)*cs^2*u^2*rho-1/12*dl^4*dt^(-1)*rho-3*dl^4*omega_3^(-3)*dt^(-1)*cs^2*rho-21*dl^4*omega_3^(-3)*dt^(-1)*u^2*rho-54*dl^4*omega_3^(-2)*dt^(-1)*cs^2*u^2*rho+9/2*dl^4*omega_3^(-2)*dt^(-1)*cs^2*rho-1/12*dl^4*dt^(-1)*cs^4*rho+63/2*dl^4*omega_3^(-2)*dt^(-1)*u^2*rho-29/12*dl^4*dt^(-1)*u^4*rho-3/2*dl^4*dt^(-1)*cs^2*u^2*rho+155/6*dl^4*omega_3^(-1)*dt^(-1)*u^4*rho-3/2*dl^4*omega_3^(-2)*dt^(-1)*rho+7/6*dl^4*omega_3^(-1)*dt^(-1)*cs^4*rho
D[1](rho) * D[1](u)
-2*dl^2*omega_3^(-1)*dt^(-1)-3*dl^2*dt^(-1)*u^2-2*dl^2*dt^(-1)*cs^2+dl^2*dt^(-1)+6*dl^2*omega_3^(-1)*dt^(-1)*u^2+4*dl^2*omega_3^(-1)*dt^(-1)*cs^2
D[1](u) * D[1](u)
-3*dl^2*dt^(-1)*u*rho+6*dl^2*omega_3^(-1)*dt^(-1)*u*rho
supp_d1q3_nse_txt/output_d1q3_nse_mrt1_symbolic_pde_00.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
1/12*(dt^(-1)*u(t,x,y,z)^3*dl^3+3*dt^(-1)*u(t,x,y,z)*cs^2*dl^3-dt^(-1)*u(t,x,y,z)*dl^3)*D[1,1,1](rho)(t,x,y,z)+dt^(-1)*u(t,x,y,z)*D[1](rho)(t,x,y,z)*dl-1/24*(6*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*dl^4+3*dt^(-1)*u(t,x,y,z)^4*dl^4-dt^(-1)*cs^2*dl^4-2*omega_3^(-1)*dt^(-1)*cs^4*dl^4-6*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^4*dl^4-3*dt^(-1)*u(t,x,y,z)^2*dl^4+12*dt^(-1)*u(t,x,y,z)^2*cs^2*dl^4-24*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*cs^2*dl^4+dt^(-1)*cs^4*dl^4+2*omega_3^(-1)*dt^(-1)*cs^2*dl^4)*D[1,1,1,1](rho)(t,x,y,z)-1/12*(5*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*dl^4+4*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^4-10*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*dl^4+3*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*cs^2*dl^4-2*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^4-6*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*cs^2*dl^4)*D[1,1,1,1](u)(t,x,y,z)+D[0](rho)(t,x,y,z)+1/12*(3*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*dl^3-dt^(-1)*rho(t,x,y,z)*dl^3+dt^(-1)*rho(t,x,y,z)*cs^2*dl^3)*D[1,1,1](u)(t,x,y,z)+dt^(-1)*rho(t,x,y,z)*D[1](u)(t,x,y,z)*dl=0
List of all coefficients of each partial derivatives:
D[1](rho)
dt^(-1)*u*dl
D[1](u)
dt^(-1)*rho*dl
D[0](rho)
1
D[1,1,1](rho)
1/12*dt^(-1)*u^3*dl^3+1/4*dt^(-1)*u*cs^2*dl^3-1/12*dt^(-1)*u*dl^3
D[1,1,1](u)
1/4*dt^(-1)*u^2*rho*dl^3-1/12*dt^(-1)*rho*dl^3+1/12*dt^(-1)*rho*cs^2*dl^3
D[1,1,1,1](rho)
-1/4*omega_3^(-1)*dt^(-1)*u^2*dl^4-1/8*dt^(-1)*u^4*dl^4+1/24*dt^(-1)*cs^2*dl^4+1/12*omega_3^(-1)*dt^(-1)*cs^4*dl^4+1/4*omega_3^(-1)*dt^(-1)*u^4*dl^4+1/8*dt^(-1)*u^2*dl^4-1/2*dt^(-1)*u^2*cs^2*dl^4+omega_3^(-1)*dt^(-1)*u^2*cs^2*dl^4-1/24*dt^(-1)*cs^4*dl^4-1/12*omega_3^(-1)*dt^(-1)*cs^2*dl^4
D[1,1,1,1](u)
-5/12*dt^(-1)*u^3*rho*dl^4-1/3*omega_3^(-1)*dt^(-1)*u*rho*dl^4+5/6*omega_3^(-1)*dt^(-1)*u^3*rho*dl^4-1/4*dt^(-1)*u*rho*cs^2*dl^4+1/6*dt^(-1)*u*rho*dl^4+1/2*omega_3^(-1)*dt^(-1)*u*rho*cs^2*dl^4
supp_d1q3_nse_txt/output_d1q3_nse_mrt1_symbolic_pde_01.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
(dt^(-1)*u(t,x,y,z)^2*dl+dt^(-1)*cs^2*dl)*D[1](rho)(t,x,y,z)-1/12*(36*omega_3^(-3)*dt^(-1)*cs^2*rho(t,x,y,z)*dl^4-432*omega_3^(-3)*dt^(-1)*cs^2*u(t,x,y,z)^2*rho(t,x,y,z)*dl^4-12*omega_3^(-3)*dt^(-1)*rho(t,x,y,z)*dl^4+252*omega_3^(-3)*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*dl^4-24*omega_3^(-3)*dt^(-1)*cs^4*rho(t,x,y,z)*dl^4+dt^(-1)*rho(t,x,y,z)*dl^4-504*omega_3^(-3)*dt^(-1)*u(t,x,y,z)^4*rho(t,x,y,z)*dl^4+18*omega_3^(-2)*dt^(-1)*rho(t,x,y,z)*dl^4+18*dt^(-1)*cs^2*u(t,x,y,z)^2*rho(t,x,y,z)*dl^4+756*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^4*rho(t,x,y,z)*dl^4+36*omega_3^(-2)*dt^(-1)*cs^4*rho(t,x,y,z)*dl^4-14*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*dl^4-14*omega_3^(-1)*dt^(-1)*cs^4*rho(t,x,y,z)*dl^4-310*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^4*rho(t,x,y,z)*dl^4-2*dt^(-1)*cs^2*rho(t,x,y,z)*dl^4+648*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)^2*rho(t,x,y,z)*dl^4-378*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*dl^4-54*omega_3^(-2)*dt^(-1)*cs^2*rho(t,x,y,z)*dl^4-252*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)^2*rho(t,x,y,z)*dl^4+29*dt^(-1)*u(t,x,y,z)^4*rho(t,x,y,z)*dl^4+22*omega_3^(-1)*dt^(-1)*cs^2*rho(t,x,y,z)*dl^4+154*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*dl^4+dt^(-1)*cs^4*rho(t,x,y,z)*dl^4-8*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*dl^4)*D[1,1,1,1](u)(t,x,y,z)-1/2*(dt^(-1)*u(t,x,y,z)^3*dl^2-6*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)*dl^2+2*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*dl^2+3*dt^(-1)*cs^2*u(t,x,y,z)*dl^2-2*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3*dl^2-dt^(-1)*u(t,x,y,z)*dl^2)*D[1,1](rho)(t,x,y,z)-1/12*(36*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^2*dl^3-12*omega_3^(-1)*dt^(-1)*cs^2*dl^3-dt^(-1)*cs^4*dl^3-12*omega_3^(-2)*dt^(-1)*cs^4*dl^3+7*dt^(-1)*u(t,x,y,z)^2*dl^3+36*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^4*dl^3-24*dt^(-1)*cs^2*u(t,x,y,z)^2*dl^3+12*omega_3^(-2)*dt^(-1)*cs^2*dl^3+144*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)^2*dl^3-7*dt^(-1)*u(t,x,y,z)^4*dl^3-36*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*dl^3-36*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^4*dl^3+12*omega_3^(-1)*dt^(-1)*cs^4*dl^3+dt^(-1)*cs^2*dl^3-144*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)^2*dl^3)*D[1,1,1](rho)(t,x,y,z)-1/12*(9*dt^(-1)*u(t,x,y,z)^5*dl^4-12*omega_3^(-3)*dt^(-1)*u(t,x,y,z)*dl^4+34*dt^(-1)*cs^2*u(t,x,y,z)^3*dl^4+216*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^5*dl^4+132*omega_3^(-3)*dt^(-1)*cs^2*u(t,x,y,z)*dl^4-144*omega_3^(-3)*dt^(-1)*u(t,x,y,z)^5*dl^4+1008*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)^3*dl^4+18*omega_3^(-2)*dt^(-1)*u(t,x,y,z)*dl^4-404*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)^3*dl^4+dt^(-1)*u(t,x,y,z)*dl^4-144*omega_3^(-3)*dt^(-1)*cs^4*u(t,x,y,z)*dl^4+98*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3*dl^4-672*omega_3^(-3)*dt^(-1)*cs^2*u(t,x,y,z)^3*dl^4-6*dt^(-1)*cs^2*u(t,x,y,z)*dl^4+156*omega_3^(-3)*dt^(-1)*u(t,x,y,z)^3*dl^4-82*omega_3^(-1)*dt^(-1)*cs^4*u(t,x,y,z)*dl^4+216*omega_3^(-2)*dt^(-1)*cs^4*u(t,x,y,z)*dl^4-90*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^5*dl^4-8*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*dl^4+5*dt^(-1)*cs^4*u(t,x,y,z)*dl^4-10*dt^(-1)*u(t,x,y,z)^3*dl^4+78*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)*dl^4-198*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)*dl^4-234*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^3*dl^4)*D[1,1,1,1](rho)(t,x,y,z)+rho(t,x,y,z)*D[0](u)(t,x,y,z)-3*D[1](u)(t,x,y,z)^2*(dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^2-2*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^2)+2*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*D[1](u)(t,x,y,z)*dl+u(t,x,y,z)*D[0](rho)(t,x,y,z)-(3*dt^(-1)*u(t,x,y,z)^2*dl^2-4*omega_3^(-1)*dt^(-1)*cs^2*dl^2-dt^(-1)*dl^2+2*dt^(-1)*cs^2*dl^2+2*omega_3^(-1)*dt^(-1)*dl^2-6*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*dl^2)*D[1](rho)(t,x,y,z)*D[1](u)(t,x,y,z)+1/6*(5*dt^(-1)*cs^2*u(t,x,y,z)*rho(t,x,y,z)*dl^3+36*omega_3^(-2)*dt^(-1)*cs^2*u(t,x,y,z)*rho(t,x,y,z)*dl^3+60*omega_3^(-2)*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*dl^3-4*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^3-60*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*dl^3+24*omega_3^(-1)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^3+11*dt^(-1)*u(t,x,y,z)^3*rho(t,x,y,z)*dl^3-36*omega_3^(-1)*dt^(-1)*cs^2*u(t,x,y,z)*rho(t,x,y,z)*dl^3-24*omega_3^(-2)*dt^(-1)*u(t,x,y,z)*rho(t,x,y,z)*dl^3)*D[1,1,1](u)(t,x,y,z)+1/2*(6*omega_3^(-1)*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*dl^2-2*omega_3^(-1)*dt^(-1)*rho(t,x,y,z)*dl^2+2*omega_3^(-1)*dt^(-1)*cs^2*rho(t,x,y,z)*dl^2-dt^(-1)*cs^2*rho(t,x,y,z)*dl^2-3*dt^(-1)*u(t,x,y,z)^2*rho(t,x,y,z)*dl^2+dt^(-1)*rho(t,x,y,z)*dl^2)*D[1,1](u)(t,x,y,z)=0
List of all coefficients of each partial derivatives:
D[1](rho)
dt^(-1)*u^2*dl+dt^(-1)*cs^2*dl
D[1](u)
2*dt^(-1)*u*rho*dl
D[0](rho)
u
D[0](u)
rho
D[1,1](rho)
-1/2*dt^(-1)*u^3*dl^2+3*omega_3^(-1)*dt^(-1)*cs^2*u*dl^2-omega_3^(-1)*dt^(-1)*u*dl^2-3/2*dt^(-1)*cs^2*u*dl^2+omega_3^(-1)*dt^(-1)*u^3*dl^2+1/2*dt^(-1)*u*dl^2
D[1,1](u)
3*omega_3^(-1)*dt^(-1)*u^2*rho*dl^2-omega_3^(-1)*dt^(-1)*rho*dl^2+omega_3^(-1)*dt^(-1)*cs^2*rho*dl^2-1/2*dt^(-1)*cs^2*rho*dl^2-3/2*dt^(-1)*u^2*rho*dl^2+1/2*dt^(-1)*rho*dl^2
D[1,1,1](rho)
-3*omega_3^(-2)*dt^(-1)*u^2*dl^3+omega_3^(-1)*dt^(-1)*cs^2*dl^3+1/12*dt^(-1)*cs^4*dl^3+omega_3^(-2)*dt^(-1)*cs^4*dl^3-7/12*dt^(-1)*u^2*dl^3-3*omega_3^(-1)*dt^(-1)*u^4*dl^3+2*dt^(-1)*cs^2*u^2*dl^3-omega_3^(-2)*dt^(-1)*cs^2*dl^3-12*omega_3^(-1)*dt^(-1)*cs^2*u^2*dl^3+7/12*dt^(-1)*u^4*dl^3+3*omega_3^(-1)*dt^(-1)*u^2*dl^3+3*omega_3^(-2)*dt^(-1)*u^4*dl^3-omega_3^(-1)*dt^(-1)*cs^4*dl^3-1/12*dt^(-1)*cs^2*dl^3+12*omega_3^(-2)*dt^(-1)*cs^2*u^2*dl^3
D[1,1,1](u)
5/6*dt^(-1)*cs^2*u*rho*dl^3+6*omega_3^(-2)*dt^(-1)*cs^2*u*rho*dl^3+10*omega_3^(-2)*dt^(-1)*u^3*rho*dl^3-2/3*dt^(-1)*u*rho*dl^3-10*omega_3^(-1)*dt^(-1)*u^3*rho*dl^3+4*omega_3^(-1)*dt^(-1)*u*rho*dl^3+11/6*dt^(-1)*u^3*rho*dl^3-6*omega_3^(-1)*dt^(-1)*cs^2*u*rho*dl^3-4*omega_3^(-2)*dt^(-1)*u*rho*dl^3
D[1,1,1,1](rho)
-3/4*dt^(-1)*u^5*dl^4+omega_3^(-3)*dt^(-1)*u*dl^4-17/6*dt^(-1)*cs^2*u^3*dl^4-18*omega_3^(-2)*dt^(-1)*u^5*dl^4-11*omega_3^(-3)*dt^(-1)*cs^2*u*dl^4+12*omega_3^(-3)*dt^(-1)*u^5*dl^4-84*omega_3^(-2)*dt^(-1)*cs^2*u^3*dl^4-3/2*omega_3^(-2)*dt^(-1)*u*dl^4+101/3*omega_3^(-1)*dt^(-1)*cs^2*u^3*dl^4-1/12*dt^(-1)*u*dl^4+12*omega_3^(-3)*dt^(-1)*cs^4*u*dl^4-49/6*omega_3^(-1)*dt^(-1)*u^3*dl^4+56*omega_3^(-3)*dt^(-1)*cs^2*u^3*dl^4+1/2*dt^(-1)*cs^2*u*dl^4-13*omega_3^(-3)*dt^(-1)*u^3*dl^4+41/6*omega_3^(-1)*dt^(-1)*cs^4*u*dl^4-18*omega_3^(-2)*dt^(-1)*cs^4*u*dl^4+15/2*omega_3^(-1)*dt^(-1)*u^5*dl^4+2/3*omega_3^(-1)*dt^(-1)*u*dl^4-5/12*dt^(-1)*cs^4*u*dl^4+5/6*dt^(-1)*u^3*dl^4-13/2*omega_3^(-1)*dt^(-1)*cs^2*u*dl^4+33/2*omega_3^(-2)*dt^(-1)*cs^2*u*dl^4+39/2*omega_3^(-2)*dt^(-1)*u^3*dl^4
D[1,1,1,1](u)
-3*omega_3^(-3)*dt^(-1)*cs^2*rho*dl^4+36*omega_3^(-3)*dt^(-1)*cs^2*u^2*rho*dl^4+omega_3^(-3)*dt^(-1)*rho*dl^4-21*omega_3^(-3)*dt^(-1)*u^2*rho*dl^4+2*omega_3^(-3)*dt^(-1)*cs^4*rho*dl^4-1/12*dt^(-1)*rho*dl^4+42*omega_3^(-3)*dt^(-1)*u^4*rho*dl^4-3/2*omega_3^(-2)*dt^(-1)*rho*dl^4-3/2*dt^(-1)*cs^2*u^2*rho*dl^4-63*omega_3^(-2)*dt^(-1)*u^4*rho*dl^4-3*omega_3^(-2)*dt^(-1)*cs^4*rho*dl^4+7/6*dt^(-1)*u^2*rho*dl^4+7/6*omega_3^(-1)*dt^(-1)*cs^4*rho*dl^4+155/6*omega_3^(-1)*dt^(-1)*u^4*rho*dl^4+1/6*dt^(-1)*cs^2*rho*dl^4-54*omega_3^(-2)*dt^(-1)*cs^2*u^2*rho*dl^4+63/2*omega_3^(-2)*dt^(-1)*u^2*rho*dl^4+9/2*omega_3^(-2)*dt^(-1)*cs^2*rho*dl^4+21*omega_3^(-1)*dt^(-1)*cs^2*u^2*rho*dl^4-29/12*dt^(-1)*u^4*rho*dl^4-11/6*omega_3^(-1)*dt^(-1)*cs^2*rho*dl^4-77/6*omega_3^(-1)*dt^(-1)*u^2*rho*dl^4-1/12*dt^(-1)*cs^4*rho*dl^4+2/3*omega_3^(-1)*dt^(-1)*rho*dl^4
D[1](rho) * D[1](u)
-3*dt^(-1)*u^2*dl^2+4*omega_3^(-1)*dt^(-1)*cs^2*dl^2+dt^(-1)*dl^2-2*dt^(-1)*cs^2*dl^2-2*omega_3^(-1)*dt^(-1)*dl^2+6*omega_3^(-1)*dt^(-1)*u^2*dl^2
D[1](u) * D[1](u)
-3*dt^(-1)*u*rho*dl^2+6*omega_3^(-1)*dt^(-1)*u*rho*dl^2
supp_d1q3_nse_txt/output_d1q3_nse_srt_symbolic_pde_00.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
u(t,x,y,z)*D[1](rho)(t,x,y,z)*dl*dt^(-1)+D[0](rho)(t,x,y,z)+1/12*D[1,1,1](rho)(t,x,y,z)*(3*cs^2*u(t,x,y,z)*dl^3*dt^(-1)+u(t,x,y,z)^3*dl^3*dt^(-1)-u(t,x,y,z)*dl^3*dt^(-1))-1/12*(rho(t,x,y,z)*dl^3*dt^(-1)-cs^2*rho(t,x,y,z)*dl^3*dt^(-1)-3*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3*dt^(-1))*D[1,1,1](u)(t,x,y,z)+1/12*(10*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1)-4*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)-3*cs^2*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)+2*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)+6*cs^2*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)-5*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1))*D[1,1,1,1](u)(t,x,y,z)+rho(t,x,y,z)*D[1](u)(t,x,y,z)*dl*dt^(-1)-1/24*D[1,1,1,1](rho)(t,x,y,z)*(6*omega^(-1)*u(t,x,y,z)^2*dl^4*dt^(-1)-cs^2*dl^4*dt^(-1)+12*cs^2*u(t,x,y,z)^2*dl^4*dt^(-1)+2*cs^2*omega^(-1)*dl^4*dt^(-1)-6*omega^(-1)*u(t,x,y,z)^4*dl^4*dt^(-1)+cs^4*dl^4*dt^(-1)+3*u(t,x,y,z)^4*dl^4*dt^(-1)-3*u(t,x,y,z)^2*dl^4*dt^(-1)-2*cs^4*omega^(-1)*dl^4*dt^(-1)-24*cs^2*omega^(-1)*u(t,x,y,z)^2*dl^4*dt^(-1))=0
List of all coefficients of each partial derivatives:
D[1](rho)
u*dl*dt^(-1)
D[1](u)
rho*dl*dt^(-1)
D[0](rho)
1
D[1,1,1](rho)
1/4*cs^2*u*dl^3*dt^(-1)+1/12*u^3*dl^3*dt^(-1)-1/12*u*dl^3*dt^(-1)
D[1,1,1](u)
-1/12*rho*dl^3*dt^(-1)+1/12*cs^2*rho*dl^3*dt^(-1)+1/4*rho*u^2*dl^3*dt^(-1)
D[1,1,1,1](rho)
-1/4*omega^(-1)*u^2*dl^4*dt^(-1)+1/24*cs^2*dl^4*dt^(-1)-1/2*cs^2*u^2*dl^4*dt^(-1)-1/12*cs^2*omega^(-1)*dl^4*dt^(-1)+1/4*omega^(-1)*u^4*dl^4*dt^(-1)-1/24*cs^4*dl^4*dt^(-1)-1/8*u^4*dl^4*dt^(-1)+1/8*u^2*dl^4*dt^(-1)+1/12*cs^4*omega^(-1)*dl^4*dt^(-1)+cs^2*omega^(-1)*u^2*dl^4*dt^(-1)
D[1,1,1,1](u)
5/6*omega^(-1)*rho*u^3*dl^4*dt^(-1)-1/3*omega^(-1)*rho*u*dl^4*dt^(-1)-1/4*cs^2*rho*u*dl^4*dt^(-1)+1/6*rho*u*dl^4*dt^(-1)+1/2*cs^2*omega^(-1)*rho*u*dl^4*dt^(-1)-5/12*rho*u^3*dl^4*dt^(-1)
supp_d1q3_nse_txt/output_d1q3_nse_srt_symbolic_pde_01.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
1/2*D[1,1](u)(t,x,y,z)*(2*omega^(-1)*rho(t,x,y,z)*dl^2*dt^(-1)*cs^2+6*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^2*dt^(-1)+rho(t,x,y,z)*dl^2*dt^(-1)-2*omega^(-1)*rho(t,x,y,z)*dl^2*dt^(-1)-3*rho(t,x,y,z)*u(t,x,y,z)^2*dl^2*dt^(-1)-rho(t,x,y,z)*dl^2*dt^(-1)*cs^2)+rho(t,x,y,z)*D[0](u)(t,x,y,z)-3*(rho(t,x,y,z)*u(t,x,y,z)*dl^2*dt^(-1)-2*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^2*dt^(-1))*D[1](u)(t,x,y,z)^2+u(t,x,y,z)*D[0](rho)(t,x,y,z)+(u(t,x,y,z)^2*dl*dt^(-1)+dl*dt^(-1)*cs^2)*D[1](rho)(t,x,y,z)-(2*omega^(-1)*dl^2*dt^(-1)+3*u(t,x,y,z)^2*dl^2*dt^(-1)+2*dl^2*dt^(-1)*cs^2-6*omega^(-1)*u(t,x,y,z)^2*dl^2*dt^(-1)-4*omega^(-1)*dl^2*dt^(-1)*cs^2-dl^2*dt^(-1))*D[1](rho)(t,x,y,z)*D[1](u)(t,x,y,z)+1/12*(36*omega^(-2)*u(t,x,y,z)^4*dl^3*dt^(-1)+144*omega^(-2)*u(t,x,y,z)^2*dl^3*dt^(-1)*cs^2+dl^3*dt^(-1)*cs^4-144*omega^(-1)*u(t,x,y,z)^2*dl^3*dt^(-1)*cs^2+12*omega^(-1)*dl^3*dt^(-1)*cs^2-7*u(t,x,y,z)^2*dl^3*dt^(-1)-36*omega^(-2)*u(t,x,y,z)^2*dl^3*dt^(-1)+12*omega^(-2)*dl^3*dt^(-1)*cs^4+7*u(t,x,y,z)^4*dl^3*dt^(-1)-36*omega^(-1)*u(t,x,y,z)^4*dl^3*dt^(-1)-12*omega^(-2)*dl^3*dt^(-1)*cs^2-dl^3*dt^(-1)*cs^2+36*omega^(-1)*u(t,x,y,z)^2*dl^3*dt^(-1)+24*u(t,x,y,z)^2*dl^3*dt^(-1)*cs^2-12*omega^(-1)*dl^3*dt^(-1)*cs^4)*D[1,1,1](rho)(t,x,y,z)-1/12*(u(t,x,y,z)*dl^4*dt^(-1)-234*omega^(-2)*u(t,x,y,z)^3*dl^4*dt^(-1)-12*omega^(-3)*u(t,x,y,z)*dl^4*dt^(-1)-90*omega^(-1)*u(t,x,y,z)^5*dl^4*dt^(-1)+78*omega^(-1)*u(t,x,y,z)*dl^4*dt^(-1)*cs^2+5*u(t,x,y,z)*dl^4*dt^(-1)*cs^4-672*omega^(-3)*u(t,x,y,z)^3*dl^4*dt^(-1)*cs^2+156*omega^(-3)*u(t,x,y,z)^3*dl^4*dt^(-1)+34*u(t,x,y,z)^3*dl^4*dt^(-1)*cs^2-144*omega^(-3)*u(t,x,y,z)*dl^4*dt^(-1)*cs^4+18*omega^(-2)*u(t,x,y,z)*dl^4*dt^(-1)-198*omega^(-2)*u(t,x,y,z)*dl^4*dt^(-1)*cs^2-10*u(t,x,y,z)^3*dl^4*dt^(-1)+1008*omega^(-2)*u(t,x,y,z)^3*dl^4*dt^(-1)*cs^2+98*omega^(-1)*u(t,x,y,z)^3*dl^4*dt^(-1)-82*omega^(-1)*u(t,x,y,z)*dl^4*dt^(-1)*cs^4-6*u(t,x,y,z)*dl^4*dt^(-1)*cs^2+132*omega^(-3)*u(t,x,y,z)*dl^4*dt^(-1)*cs^2+216*omega^(-2)*u(t,x,y,z)*dl^4*dt^(-1)*cs^4-404*omega^(-1)*u(t,x,y,z)^3*dl^4*dt^(-1)*cs^2+216*omega^(-2)*u(t,x,y,z)^5*dl^4*dt^(-1)+9*u(t,x,y,z)^5*dl^4*dt^(-1)-144*omega^(-3)*u(t,x,y,z)^5*dl^4*dt^(-1)-8*omega^(-1)*u(t,x,y,z)*dl^4*dt^(-1))*D[1,1,1,1](rho)(t,x,y,z)-1/12*(29*rho(t,x,y,z)*u(t,x,y,z)^4*dl^4*dt^(-1)+18*rho(t,x,y,z)*u(t,x,y,z)^2*dl^4*dt^(-1)*cs^2-504*omega^(-3)*rho(t,x,y,z)*u(t,x,y,z)^4*dl^4*dt^(-1)-14*rho(t,x,y,z)*u(t,x,y,z)^2*dl^4*dt^(-1)-24*omega^(-3)*rho(t,x,y,z)*dl^4*dt^(-1)*cs^4-54*omega^(-2)*rho(t,x,y,z)*dl^4*dt^(-1)*cs^2+rho(t,x,y,z)*dl^4*dt^(-1)*cs^4-432*omega^(-3)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^4*dt^(-1)*cs^2+22*omega^(-1)*rho(t,x,y,z)*dl^4*dt^(-1)*cs^2-8*omega^(-1)*rho(t,x,y,z)*dl^4*dt^(-1)+252*omega^(-3)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^4*dt^(-1)+36*omega^(-3)*rho(t,x,y,z)*dl^4*dt^(-1)*cs^2-12*omega^(-3)*rho(t,x,y,z)*dl^4*dt^(-1)+36*omega^(-2)*rho(t,x,y,z)*dl^4*dt^(-1)*cs^4+154*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^4*dt^(-1)+rho(t,x,y,z)*dl^4*dt^(-1)-378*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^4*dt^(-1)-2*rho(t,x,y,z)*dl^4*dt^(-1)*cs^2-252*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^4*dt^(-1)*cs^2-14*omega^(-1)*rho(t,x,y,z)*dl^4*dt^(-1)*cs^4-310*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)^4*dl^4*dt^(-1)+648*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^4*dt^(-1)*cs^2+18*omega^(-2)*rho(t,x,y,z)*dl^4*dt^(-1)+756*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)^4*dl^4*dt^(-1))*D[1,1,1,1](u)(t,x,y,z)+1/2*(6*omega^(-1)*u(t,x,y,z)*dl^2*dt^(-1)*cs^2+2*omega^(-1)*u(t,x,y,z)^3*dl^2*dt^(-1)-2*omega^(-1)*u(t,x,y,z)*dl^2*dt^(-1)+u(t,x,y,z)*dl^2*dt^(-1)-3*u(t,x,y,z)*dl^2*dt^(-1)*cs^2-u(t,x,y,z)^3*dl^2*dt^(-1))*D[1,1](rho)(t,x,y,z)+2*rho(t,x,y,z)*u(t,x,y,z)*D[1](u)(t,x,y,z)*dl*dt^(-1)+1/6*D[1,1,1](u)(t,x,y,z)*(11*rho(t,x,y,z)*u(t,x,y,z)^3*dl^3*dt^(-1)-4*rho(t,x,y,z)*u(t,x,y,z)*dl^3*dt^(-1)+5*rho(t,x,y,z)*u(t,x,y,z)*dl^3*dt^(-1)*cs^2-24*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)*dl^3*dt^(-1)+24*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^3*dt^(-1)+36*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)*dl^3*dt^(-1)*cs^2-36*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^3*dt^(-1)*cs^2-60*omega^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^3*dt^(-1)+60*omega^(-2)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^3*dt^(-1))=0
List of all coefficients of each partial derivatives:
D[1](rho)
u^2*dl*dt^(-1)+dl*dt^(-1)*cs^2
D[1](u)
2*rho*u*dl*dt^(-1)
D[0](rho)
u
D[0](u)
rho
D[1,1](rho)
3*omega^(-1)*u*dl^2*dt^(-1)*cs^2+omega^(-1)*u^3*dl^2*dt^(-1)-omega^(-1)*u*dl^2*dt^(-1)+1/2*u*dl^2*dt^(-1)-3/2*u*dl^2*dt^(-1)*cs^2-1/2*u^3*dl^2*dt^(-1)
D[1,1](u)
omega^(-1)*rho*dl^2*dt^(-1)*cs^2+3*omega^(-1)*rho*u^2*dl^2*dt^(-1)+1/2*rho*dl^2*dt^(-1)-omega^(-1)*rho*dl^2*dt^(-1)-3/2*rho*u^2*dl^2*dt^(-1)-1/2*rho*dl^2*dt^(-1)*cs^2
D[1,1,1](rho)
3*omega^(-2)*u^4*dl^3*dt^(-1)+12*omega^(-2)*u^2*dl^3*dt^(-1)*cs^2+1/12*dl^3*dt^(-1)*cs^4-12*omega^(-1)*u^2*dl^3*dt^(-1)*cs^2+omega^(-1)*dl^3*dt^(-1)*cs^2-7/12*u^2*dl^3*dt^(-1)-3*omega^(-2)*u^2*dl^3*dt^(-1)+omega^(-2)*dl^3*dt^(-1)*cs^4+7/12*u^4*dl^3*dt^(-1)-3*omega^(-1)*u^4*dl^3*dt^(-1)-omega^(-2)*dl^3*dt^(-1)*cs^2-1/12*dl^3*dt^(-1)*cs^2+3*omega^(-1)*u^2*dl^3*dt^(-1)+2*u^2*dl^3*dt^(-1)*cs^2-omega^(-1)*dl^3*dt^(-1)*cs^4
D[1,1,1](u)
11/6*rho*u^3*dl^3*dt^(-1)-2/3*rho*u*dl^3*dt^(-1)+5/6*rho*u*dl^3*dt^(-1)*cs^2-4*omega^(-2)*rho*u*dl^3*dt^(-1)+4*omega^(-1)*rho*u*dl^3*dt^(-1)+6*omega^(-2)*rho*u*dl^3*dt^(-1)*cs^2-6*omega^(-1)*rho*u*dl^3*dt^(-1)*cs^2-10*omega^(-1)*rho*u^3*dl^3*dt^(-1)+10*omega^(-2)*rho*u^3*dl^3*dt^(-1)
D[1,1,1,1](rho)
-1/12*u*dl^4*dt^(-1)+39/2*omega^(-2)*u^3*dl^4*dt^(-1)+omega^(-3)*u*dl^4*dt^(-1)+15/2*omega^(-1)*u^5*dl^4*dt^(-1)-13/2*omega^(-1)*u*dl^4*dt^(-1)*cs^2-5/12*u*dl^4*dt^(-1)*cs^4+56*omega^(-3)*u^3*dl^4*dt^(-1)*cs^2-13*omega^(-3)*u^3*dl^4*dt^(-1)-17/6*u^3*dl^4*dt^(-1)*cs^2+12*omega^(-3)*u*dl^4*dt^(-1)*cs^4-3/2*omega^(-2)*u*dl^4*dt^(-1)+33/2*omega^(-2)*u*dl^4*dt^(-1)*cs^2+5/6*u^3*dl^4*dt^(-1)-84*omega^(-2)*u^3*dl^4*dt^(-1)*cs^2-49/6*omega^(-1)*u^3*dl^4*dt^(-1)+41/6*omega^(-1)*u*dl^4*dt^(-1)*cs^4+1/2*u*dl^4*dt^(-1)*cs^2-11*omega^(-3)*u*dl^4*dt^(-1)*cs^2-18*omega^(-2)*u*dl^4*dt^(-1)*cs^4+101/3*omega^(-1)*u^3*dl^4*dt^(-1)*cs^2-18*omega^(-2)*u^5*dl^4*dt^(-1)-3/4*u^5*dl^4*dt^(-1)+12*omega^(-3)*u^5*dl^4*dt^(-1)+2/3*omega^(-1)*u*dl^4*dt^(-1)
D[1,1,1,1](u)
-29/12*rho*u^4*dl^4*dt^(-1)-3/2*rho*u^2*dl^4*dt^(-1)*cs^2+42*omega^(-3)*rho*u^4*dl^4*dt^(-1)+7/6*rho*u^2*dl^4*dt^(-1)+2*omega^(-3)*rho*dl^4*dt^(-1)*cs^4+9/2*omega^(-2)*rho*dl^4*dt^(-1)*cs^2-1/12*rho*dl^4*dt^(-1)*cs^4+36*omega^(-3)*rho*u^2*dl^4*dt^(-1)*cs^2-11/6*omega^(-1)*rho*dl^4*dt^(-1)*cs^2+2/3*omega^(-1)*rho*dl^4*dt^(-1)-21*omega^(-3)*rho*u^2*dl^4*dt^(-1)-3*omega^(-3)*rho*dl^4*dt^(-1)*cs^2+omega^(-3)*rho*dl^4*dt^(-1)-3*omega^(-2)*rho*dl^4*dt^(-1)*cs^4-77/6*omega^(-1)*rho*u^2*dl^4*dt^(-1)-1/12*rho*dl^4*dt^(-1)+63/2*omega^(-2)*rho*u^2*dl^4*dt^(-1)+1/6*rho*dl^4*dt^(-1)*cs^2+21*omega^(-1)*rho*u^2*dl^4*dt^(-1)*cs^2+7/6*omega^(-1)*rho*dl^4*dt^(-1)*cs^4+155/6*omega^(-1)*rho*u^4*dl^4*dt^(-1)-54*omega^(-2)*rho*u^2*dl^4*dt^(-1)*cs^2-3/2*omega^(-2)*rho*dl^4*dt^(-1)-63*omega^(-2)*rho*u^4*dl^4*dt^(-1)
D[1](rho) * D[1](u)
-2*omega^(-1)*dl^2*dt^(-1)-3*u^2*dl^2*dt^(-1)-2*dl^2*dt^(-1)*cs^2+6*omega^(-1)*u^2*dl^2*dt^(-1)+4*omega^(-1)*dl^2*dt^(-1)*cs^2+dl^2*dt^(-1)
D[1](u) * D[1](u)
-3*rho*u*dl^2*dt^(-1)+6*omega^(-1)*rho*u*dl^2*dt^(-1)
supp_d2q5_ade_txt/output_d2q5_ade_clbm1_symbolic_pde_00.txt 0 → 100644
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supp_d2q5_ade_txt/output_d2q5_ade_mrt1_symbolic_pde_00.txt 0 → 100644
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supp_d2q5_ade_txt/output_d2q5_ade_mrt2_symbolic_pde_00.txt 0 → 100644
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supp_d2q5_ade_txt/output_d2q5_ade_srt_symbolic_pde_00.txt 0 → 100644
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supp_d2q9_nse_txt/output_d2q9_nse_clbm1_symbolic_pde_00.txt 0 → 100644
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Complete expression of PDE that can be directly imported to Maxima:
-1/12*(dl^3*dt^(-1)*v(t,x,y,z)-3*dl^3*dt^(-1)*v(t,x,y,z)*cs^2-dl^3*dt^(-1)*v(t,x,y,z)^3)*D[2,2,2](rho)(t,x,y,z)+rho(t,x,y,z)*dl*D[1](u)(t,x,y,z)*dt^(-1)+u(t,x,y,z)*dl*D[1](rho)(t,x,y,z)*dt^(-1)+dl*D[2](rho)(t,x,y,z)*dt^(-1)*v(t,x,y,z)+1/12*(rho(t,x,y,z)*dl^3*dt^(-1)*cs^2-rho(t,x,y,z)*dl^3*dt^(-1)+3*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3*dt^(-1))*D[1,1,1](u)(t,x,y,z)+1/24*(3*u(t,x,y,z)^2*dl^4*dt^(-1)-6*omega_5^(-1)*u(t,x,y,z)^2*dl^4*dt^(-1)-3*u(t,x,y,z)^4*dl^4*dt^(-1)+6*omega_5^(-1)*u(t,x,y,z)^4*dl^4*dt^(-1)+2*omega_5^(-1)*dl^4*dt^(-1)*cs^4-dl^4*dt^(-1)*cs^4+24*omega_5^(-1)*u(t,x,y,z)^2*dl^4*dt^(-1)*cs^2+dl^4*dt^(-1)*cs^2-12*u(t,x,y,z)^2*dl^4*dt^(-1)*cs^2-2*omega_5^(-1)*dl^4*dt^(-1)*cs^2)*D[1,1,1,1](rho)(t,x,y,z)+rho(t,x,y,z)*dl*D[2](v)(t,x,y,z)*dt^(-1)+1/12*(rho(t,x,y,z)*dl^3*dt^(-1)*cs^2-rho(t,x,y,z)*dl^3*dt^(-1)+3*rho(t,x,y,z)*dl^3*dt^(-1)*v(t,x,y,z)^2)*D[2,2,2](v)(t,x,y,z)-1/6*rho(t,x,y,z)*dl^3*D[1,2,2](u)(t,x,y,z)*dt^(-1)*cs^2-1/6*(2*dl^4*dt^(-1)*omega_4^(-1)*cs^4-dl^4*dt^(-1)*cs^4)*D[1,1,2,2](rho)(t,x,y,z)+1/12*(6*omega_5^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*cs^2-4*omega_5^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)+2*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)-3*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*cs^2-5*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1)+10*omega_5^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1))*D[1,1,1,1](u)(t,x,y,z)+1/12*(3*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*omega_7^(-1)+3*omega_5^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*cs^2-omega_5^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)-rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)+3*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*cs^2+rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1)-3*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1)*omega_7^(-1)-9*rho(t,x,y,z)*u(t,x,y,z)*dl^4*dt^(-1)*omega_7^(-1)*cs^2+omega_5^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4*dt^(-1))*D[1,1,1,2](v)(t,x,y,z)-1/12*(u(t,x,y,z)*dl^3*dt^(-1)-u(t,x,y,z)^3*dl^3*dt^(-1)-3*u(t,x,y,z)*dl^3*dt^(-1)*cs^2)*D[1,1,1](rho)(t,x,y,z)+1/12*D[2,2,2,2](v)(t,x,y,z)*(6*rho(t,x,y,z)*dl^4*omega_6^(-1)*dt^(-1)*v(t,x,y,z)*cs^2+2*rho(t,x,y,z)*dl^4*dt^(-1)*v(t,x,y,z)-5*rho(t,x,y,z)*dl^4*dt^(-1)*v(t,x,y,z)^3+10*rho(t,x,y,z)*dl^4*omega_6^(-1)*dt^(-1)*v(t,x,y,z)^3-4*rho(t,x,y,z)*dl^4*omega_6^(-1)*dt^(-1)*v(t,x,y,z)-3*rho(t,x,y,z)*dl^4*dt^(-1)*v(t,x,y,z)*cs^2)+1/24*(2*dl^4*omega_6^(-1)*dt^(-1)*cs^4+3*dl^4*dt^(-1)*v(t,x,y,z)^2+24*dl^4*omega_6^(-1)*dt^(-1)*v(t,x,y,z)^2*cs^2-6*dl^4*omega_6^(-1)*dt^(-1)*v(t,x,y,z)^2-dl^4*dt^(-1)*cs^4+6*dl^4*omega_6^(-1)*dt^(-1)*v(t,x,y,z)^4+dl^4*dt^(-1)*cs^2-2*dl^4*omega_6^(-1)*dt^(-1)*cs^2-12*dl^4*dt^(-1)*v(t,x,y,z)^2*cs^2-3*dl^4*dt^(-1)*v(t,x,y,z)^4)*D[2,2,2,2](rho)(t,x,y,z)+D[0](rho)(t,x,y,z)+1/12*(3*rho(t,x,y,z)*dl^4*omega_6^(-1)*dt^(-1)*v(t,x,y,z)*cs^2-rho(t,x,y,z)*dl^4*dt^(-1)*v(t,x,y,z)+rho(t,x,y,z)*dl^4*dt^(-1)*v(t,x,y,z)^3+rho(t,x,y,z)*dl^4*omega_6^(-1)*dt^(-1)*v(t,x,y,z)^3+3*omega_8^(-1)*rho(t,x,y,z)*dl^4*dt^(-1)*v(t,x,y,z)-rho(t,x,y,z)*dl^4*omega_6^(-1)*dt^(-1)*v(t,x,y,z)-9*omega_8^(-1)*rho(t,x,y,z)*dl^4*dt^(-1)*v(t,x,y,z)*cs^2+3*rho(t,x,y,z)*dl^4*dt^(-1)*v(t,x,y,z)*cs^2-3*omega_8^(-1)*rho(t,x,y,z)*dl^4*dt^(-1)*v(t,x,y,z)^3)*D[1,2,2,2](u)(t,x,y,z)-1/6*rho(t,x,y,z)*dl^3*D[1,1,2](v)(t,x,y,z)*dt^(-1)*cs^2=0
List of all coefficients of each partial derivatives:
D[2](rho)
dl*dt^(-1)*v
D[2](v)
rho*dl*dt^(-1)
D[1](rho)
u*dl*dt^(-1)
D[1](u)
rho*dl*dt^(-1)
D[0](rho)
1
D[2,2,2](rho)
-1/12*dl^3*dt^(-1)*v+1/4*dl^3*dt^(-1)*v*cs^2+1/12*dl^3*dt^(-1)*v^3
D[2,2,2](v)
1/12*rho*dl^3*dt^(-1)*cs^2-1/12*rho*dl^3*dt^(-1)+1/4*rho*dl^3*dt^(-1)*v^2
D[1,2,2](u)
-1/6*rho*dl^3*dt^(-1)*cs^2
D[1,1,2](v)
-1/6*rho*dl^3*dt^(-1)*cs^2
D[1,1,1](rho)
-1/12*u*dl^3*dt^(-1)+1/12*u^3*dl^3*dt^(-1)+1/4*u*dl^3*dt^(-1)*cs^2
D[1,1,1](u)
1/12*rho*dl^3*dt^(-1)*cs^2-1/12*rho*dl^3*dt^(-1)+1/4*rho*u^2*dl^3*dt^(-1)
D[2,2,2,2](rho)
1/12*dl^4*omega_6^(-1)*dt^(-1)*cs^4+1/8*dl^4*dt^(-1)*v^2+dl^4*omega_6^(-1)*dt^(-1)*v^2*cs^2-1/4*dl^4*omega_6^(-1)*dt^(-1)*v^2-1/24*dl^4*dt^(-1)*cs^4+1/4*dl^4*omega_6^(-1)*dt^(-1)*v^4+1/24*dl^4*dt^(-1)*cs^2-1/12*dl^4*omega_6^(-1)*dt^(-1)*cs^2-1/2*dl^4*dt^(-1)*v^2*cs^2-1/8*dl^4*dt^(-1)*v^4
D[2,2,2,2](v)
1/2*rho*dl^4*omega_6^(-1)*dt^(-1)*v*cs^2+1/6*rho*dl^4*dt^(-1)*v-5/12*rho*dl^4*dt^(-1)*v^3+5/6*rho*dl^4*omega_6^(-1)*dt^(-1)*v^3-1/3*rho*dl^4*omega_6^(-1)*dt^(-1)*v-1/4*rho*dl^4*dt^(-1)*v*cs^2
D[1,2,2,2](u)
1/4*rho*dl^4*omega_6^(-1)*dt^(-1)*v*cs^2-1/12*rho*dl^4*dt^(-1)*v+1/12*rho*dl^4*dt^(-1)*v^3+1/12*rho*dl^4*omega_6^(-1)*dt^(-1)*v^3+1/4*omega_8^(-1)*rho*dl^4*dt^(-1)*v-1/12*rho*dl^4*omega_6^(-1)*dt^(-1)*v-3/4*omega_8^(-1)*rho*dl^4*dt^(-1)*v*cs^2+1/4*rho*dl^4*dt^(-1)*v*cs^2-1/4*omega_8^(-1)*rho*dl^4*dt^(-1)*v^3
D[1,1,2,2](rho)
-1/3*dl^4*dt^(-1)*omega_4^(-1)*cs^4+1/6*dl^4*dt^(-1)*cs^4
D[1,1,1,2](v)
1/4*rho*u*dl^4*dt^(-1)*omega_7^(-1)+1/4*omega_5^(-1)*rho*u*dl^4*dt^(-1)*cs^2-1/12*omega_5^(-1)*rho*u*dl^4*dt^(-1)-1/12*rho*u*dl^4*dt^(-1)+1/4*rho*u*dl^4*dt^(-1)*cs^2+1/12*rho*u^3*dl^4*dt^(-1)-1/4*rho*u^3*dl^4*dt^(-1)*omega_7^(-1)-3/4*rho*u*dl^4*dt^(-1)*omega_7^(-1)*cs^2+1/12*omega_5^(-1)*rho*u^3*dl^4*dt^(-1)
D[1,1,1,1](rho)
1/8*u^2*dl^4*dt^(-1)-1/4*omega_5^(-1)*u^2*dl^4*dt^(-1)-1/8*u^4*dl^4*dt^(-1)+1/4*omega_5^(-1)*u^4*dl^4*dt^(-1)+1/12*omega_5^(-1)*dl^4*dt^(-1)*cs^4-1/24*dl^4*dt^(-1)*cs^4+omega_5^(-1)*u^2*dl^4*dt^(-1)*cs^2+1/24*dl^4*dt^(-1)*cs^2-1/2*u^2*dl^4*dt^(-1)*cs^2-1/12*omega_5^(-1)*dl^4*dt^(-1)*cs^2
D[1,1,1,1](u)
1/2*omega_5^(-1)*rho*u*dl^4*dt^(-1)*cs^2-1/3*omega_5^(-1)*rho*u*dl^4*dt^(-1)+1/6*rho*u*dl^4*dt^(-1)-1/4*rho*u*dl^4*dt^(-1)*cs^2-5/12*rho*u^3*dl^4*dt^(-1)+5/6*omega_5^(-1)*rho*u^3*dl^4*dt^(-1)
supp_d2q9_nse_txt/output_d2q9_nse_clbm1_symbolic_pde_01.txt 0 → 100644
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supp_d2q9_nse_txt/output_d2q9_nse_clbm1_symbolic_pde_02.txt 0 → 100644
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supp_d2q9_nse_txt/output_d2q9_nse_clbm2_symbolic_pde_00.txt 0 → 100644
View file @ f5103a6c
Complete expression of PDE that can be directly imported to Maxima:
-1/6*dt^(-1)*cs^2*rho(t,x,y,z)*D[1,2,2](u)(t,x,y,z)*dl^3+dt^(-1)*v(t,x,y,z)*D[2](rho)(t,x,y,z)*dl-1/6*(2*dt^(-1)*omega_4^(-1)*cs^4*dl^4-dt^(-1)*cs^4*dl^4)*D[1,1,2,2](rho)(t,x,y,z)-1/12*(dt^(-1)*u(t,x,y,z)*dl^3-dt^(-1)*u(t,x,y,z)^3*dl^3-3*dt^(-1)*cs^2*u(t,x,y,z)*dl^3)*D[1,1,1](rho)(t,x,y,z)+1/24*(2*omega_6^(-1)*dt^(-1)*cs^4*dl^4+dt^(-1)*cs^2*dl^4+3*dt^(-1)*v(t,x,y,z)^2*dl^4+6*omega_6^(-1)*dt^(-1)*v(t,x,y,z)^4*dl^4-12*dt^(-1)*cs^2*v(t,x,y,z)^2*dl^4+24*omega_6^(-1)*dt^(-1)*cs^2*v(t,x,y,z)^2*dl^4-2*omega_6^(-1)*dt^(-1)*cs^2*dl^4-dt^(-1)*cs^4*dl^4-3*dt^(-1)*v(t,x,y,z)^4*dl^4-6*omega_6^(-1)*dt^(-1)*v(t,x,y,z)^2*dl^4)*D[2,2,2,2](rho)(t,x,y,z)+1/12*(dt^(-1)*cs^2*rho(t,x,y,z)*dl^3-dt^(-1)*rho(t,x,y,z)*dl^3+3*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^2*dl^3)*D[1,1,1](u)(t,x,y,z)+1/12*(dt^(-1)*cs^2*rho(t,x,y,z)*dl^3+3*dt^(-1)*rho(t,x,y,z)*v(t,x,y,z)^2*dl^3-dt^(-1)*rho(t,x,y,z)*dl^3)*D[2,2,2](v)(t,x,y,z)-1/24*(6*dt^(-1)*u(t,x,y,z)^2*omega_5^(-1)*dl^4-3*dt^(-1)*u(t,x,y,z)^2*dl^4-6*dt^(-1)*u(t,x,y,z)^4*omega_5^(-1)*dl^4-dt^(-1)*cs^2*dl^4-24*dt^(-1)*cs^2*u(t,x,y,z)^2*omega_5^(-1)*dl^4+3*dt^(-1)*u(t,x,y,z)^4*dl^4+2*dt^(-1)*cs^2*omega_5^(-1)*dl^4+12*dt^(-1)*cs^2*u(t,x,y,z)^2*dl^4+dt^(-1)*cs^4*dl^4-2*dt^(-1)*cs^4*omega_5^(-1)*dl^4)*D[1,1,1,1](rho)(t,x,y,z)-1/12*(3*dt^(-1)*omega_7^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4-3*dt^(-1)*cs^2*rho(t,x,y,z)*u(t,x,y,z)*dl^4-dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4+dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*omega_5^(-1)*dl^4-3*dt^(-1)*omega_7^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4-3*dt^(-1)*cs^2*rho(t,x,y,z)*u(t,x,y,z)*omega_5^(-1)*dl^4+dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4+9*dt^(-1)*omega_7^(-1)*cs^2*rho(t,x,y,z)*u(t,x,y,z)*dl^4-dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*omega_5^(-1)*dl^4)*D[1,1,1,2](v)(t,x,y,z)-1/12*(3*dt^(-1)*cs^2*rho(t,x,y,z)*v(t,x,y,z)*dl^4+5*dt^(-1)*rho(t,x,y,z)*v(t,x,y,z)^3*dl^4-10*omega_6^(-1)*dt^(-1)*rho(t,x,y,z)*v(t,x,y,z)^3*dl^4-2*dt^(-1)*rho(t,x,y,z)*v(t,x,y,z)*dl^4-6*omega_6^(-1)*dt^(-1)*cs^2*rho(t,x,y,z)*v(t,x,y,z)*dl^4+4*omega_6^(-1)*dt^(-1)*rho(t,x,y,z)*v(t,x,y,z)*dl^4)*D[2,2,2,2](v)(t,x,y,z)+1/12*(3*dt^(-1)*cs^2*rho(t,x,y,z)*v(t,x,y,z)*dl^4-3*dt^(-1)*omega_8^(-1)*rho(t,x,y,z)*v(t,x,y,z)^3*dl^4+dt^(-1)*rho(t,x,y,z)*v(t,x,y,z)^3*dl^4+omega_6^(-1)*dt^(-1)*rho(t,x,y,z)*v(t,x,y,z)^3*dl^4-9*dt^(-1)*cs^2*omega_8^(-1)*rho(t,x,y,z)*v(t,x,y,z)*dl^4-dt^(-1)*rho(t,x,y,z)*v(t,x,y,z)*dl^4+3*dt^(-1)*omega_8^(-1)*rho(t,x,y,z)*v(t,x,y,z)*dl^4+3*omega_6^(-1)*dt^(-1)*cs^2*rho(t,x,y,z)*v(t,x,y,z)*dl^4-omega_6^(-1)*dt^(-1)*rho(t,x,y,z)*v(t,x,y,z)*dl^4)*D[1,2,2,2](u)(t,x,y,z)+dt^(-1)*u(t,x,y,z)*D[1](rho)(t,x,y,z)*dl-1/12*(dt^(-1)*v(t,x,y,z)*dl^3-3*dt^(-1)*cs^2*v(t,x,y,z)*dl^3-dt^(-1)*v(t,x,y,z)^3*dl^3)*D[2,2,2](rho)(t,x,y,z)+dt^(-1)*rho(t,x,y,z)*D[1](u)(t,x,y,z)*dl-1/6*dt^(-1)*cs^2*rho(t,x,y,z)*dl^3*D[1,1,2](v)(t,x,y,z)+D[0](rho)(t,x,y,z)-1/12*(3*dt^(-1)*cs^2*rho(t,x,y,z)*u(t,x,y,z)*dl^4+5*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*dl^4+4*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*omega_5^(-1)*dl^4-6*dt^(-1)*cs^2*rho(t,x,y,z)*u(t,x,y,z)*omega_5^(-1)*dl^4-2*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)*dl^4-10*dt^(-1)*rho(t,x,y,z)*u(t,x,y,z)^3*omega_5^(-1)*dl^4)*D[1,1,1,1](u)(t,x,y,z)+dt^(-1)*rho(t,x,y,z)*dl*D[2](v)(t,x,y,z)=0
List of all coefficients of each partial derivatives:
D[2](rho)
dt^(-1)*v*dl
D[2](v)
dt^(-1)*rho*dl
D[1](rho)
dt^(-1)*u*dl
D[1](u)
dt^(-1)*rho*dl
D[0](rho)
1
D[2,2,2](rho)
-1/12*dt^(-1)*v*dl^3+1/4*dt^(-1)*cs^2*v*dl^3+1/12*dt^(-1)*v^3*dl^3
D[2,2,2](v)
1/12*dt^(-1)*cs^2*rho*dl^3+1/4*dt^(-1)*rho*v^2*dl^3-1/12*dt^(-1)*rho*dl^3
D[1,2,2](u)
-1/6*dt^(-1)*cs^2*rho*dl^3
D[1,1,2](v)
-1/6*dt^(-1)*cs^2*rho*dl^3
D[1,1,1](rho)
-1/12*dt^(-1)*u*dl^3+1/12*dt^(-1)*u^3*dl^3+1/4*dt^(-1)*cs^2*u*dl^3
D[1,1,1](u)
1/12*dt^(-1)*cs^2*rho*dl^3-1/12*dt^(-1)*rho*dl^3+1/4*dt^(-1)*rho*u^2*dl^3
D[2,2,2,2](rho)
1/12*omega_6^(-1)*dt^(-1)*cs^4*dl^4+1/24*dt^(-1)*cs^2*dl^4+1/8*dt^(-1)*v^2*dl^4+1/4*omega_6^(-1)*dt^(-1)*v^4*dl^4-1/2*dt^(-1)*cs^2*v^2*dl^4+omega_6^(-1)*dt^(-1)*cs^2*v^2*dl^4-1/12*omega_6^(-1)*dt^(-1)*cs^2*dl^4-1/24*dt^(-1)*cs^4*dl^4-1/8*dt^(-1)*v^4*dl^4-1/4*omega_6^(-1)*dt^(-1)*v^2*dl^4
D[2,2,2,2](v)
-1/4*dt^(-1)*cs^2*rho*v*dl^4-5/12*dt^(-1)*rho*v^3*dl^4+5/6*omega_6^(-1)*dt^(-1)*rho*v^3*dl^4+1/6*dt^(-1)*rho*v*dl^4+1/2*omega_6^(-1)*dt^(-1)*cs^2*rho*v*dl^4-1/3*omega_6^(-1)*dt^(-1)*rho*v*dl^4
D[1,2,2,2](u)
1/4*dt^(-1)*cs^2*rho*v*dl^4-1/4*dt^(-1)*omega_8^(-1)*rho*v^3*dl^4+1/12*dt^(-1)*rho*v^3*dl^4+1/12*omega_6^(-1)*dt^(-1)*rho*v^3*dl^4-3/4*dt^(-1)*cs^2*omega_8^(-1)*rho*v*dl^4-1/12*dt^(-1)*rho*v*dl^4+1/4*dt^(-1)*omega_8^(-1)*rho*v*dl^4+1/4*omega_6^(-1)*dt^(-1)*cs^2*rho*v*dl^4-1/12*omega_6^(-1)*dt^(-1)*rho*v*dl^4
D[1,1,2,2](rho)
-1/3*dt^(-1)*omega_4^(-1)*cs^4*dl^4+1/6*dt^(-1)*cs^4*dl^4
D[1,1,1,2](v)
-1/4*dt^(-1)*omega_7^(-1)*rho*u^3*dl^4+1/4*dt^(-1)*cs^2*rho*u*dl^4+1/12*dt^(-1)*rho*u^3*dl^4-1/12*dt^(-1)*rho*u*omega_5^(-1)*dl^4+1/4*dt^(-1)*omega_7^(-1)*rho*u*dl^4+1/4*dt^(-1)*cs^2*rho*u*omega_5^(-1)*dl^4-1/12*dt^(-1)*rho*u*dl^4-3/4*dt^(-1)*omega_7^(-1)*cs^2*rho*u*dl^4+1/12*dt^(-1)*rho*u^3*omega_5^(-1)*dl^4
D[1,1,1,1](rho)
-1/4*dt^(-1)*u^2*omega_5^(-1)*dl^4+1/8*dt^(-1)*u^2*dl^4+1/4*dt^(-1)*u^4*omega_5^(-1)*dl^4+1/24*dt^(-1)*cs^2*dl^4+dt^(-1)*cs^2*u^2*omega_5^(-1)*dl^4-1/8*dt^(-1)*u^4*dl^4-1/12*dt^(-1)*cs^2*omega_5^(-1)*dl^4-1/2*dt^(-1)*cs^2*u^2*dl^4-1/24*dt^(-1)*cs^4*dl^4+1/12*dt^(-1)*cs^4*omega_5^(-1)*dl^4
D[1,1,1,1](u)
-1/4*dt^(-1)*cs^2*rho*u*dl^4-5/12*dt^(-1)*rho*u^3*dl^4-1/3*dt^(-1)*rho*u*omega_5^(-1)*dl^4+1/2*dt^(-1)*cs^2*rho*u*omega_5^(-1)*dl^4+1/6*dt^(-1)*rho*u*dl^4+5/6*dt^(-1)*rho*u^3*omega_5^(-1)*dl^4
supp_d2q9_nse_txt/output_d2q9_nse_clbm2_symbolic_pde_01.txt 0 → 100644
View file @ f5103a6c
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supp_d2q9_nse_txt/output_d2q9_nse_clbm2_symbolic_pde_02.txt 0 → 100644
View file @ f5103a6c
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