My Matlab code for 1D convection Diffusion problem is taking too much time to execute

Question

Rajat Powade 2021-8-31

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1443774-my-matlab-code-for-1d-convection-diffusion-problem-is-taking-too-much-time-to-execute

回答： the cyclist 2021-9-1

clc;
clear all;
phia=1; %Boundary Conditions
phib=0; %Boundary Conditions
gamma=0.1;
L=1; %Length of a bar
nx=5; %No. of subdomains
dx=L/nx; %finite volume length
phi=zeros(nx+2,1); 
u=0.1;
rho=1;
D=gamma/dx;
F=rho*u;
tolearnce=1e-7;
error=1;
phi(1,1)=phia;
phi(7,1)=phib;
iter=0;
x=0:dx:L;
% p= rho*u*L/gamma;
phi_exact = phia + (phib-phia).*((exp(rho*u*x/gamma)-1)./ (exp(rho*u*L/gamma)-1));
figure (1);
plot(x,phi_exact,'ro')
while error>tolearnce
 phi_old=phi;
 for i=2
     a_E1=D-F/2;
     a_W1=0;
     Spa=-(2*D+F);
     Sua=(2*D+F)*phia;
     a_P1=a_E1+a_W1-Spa;
     phi(i,1)=(a_E1*phi(i+1) + a_W1*phi(i-1)+ Sua)/a_P1;
 end
 
 for i=3:nx
     a_W2=D+F/2;
     a_E2=D-F/2;
     a_P2=2*D;
     phi(i,1)=(a_E2*phi(i+1) + a_W2*phi(i-1))/a_P2;
 end
 for i=6
     a_W3=D+F/2;
     a_E3=0;
     Spb=-(2*D-F);
     Sub=(2*D-F)*phib;
     a_P3=a_E3+a_W3-Spb;
     phi(i,1)=(a_E3*phi(i+1) + a_W3*phi(i-1)+ Sub)/a_P3;
 end
 iter=iter+1;
end
figure(1)
hold on
plot(x,phi,'b','Linewidth',1);
legend('Exact solution','Difference_Scheme');