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Meteb Mejbel on 5 Jul 2021
Answered: Meteb Mejbel on 5 Jul 2021
Hi all,
I am trying to solve a system of multivariables pdes using pdepe solver. Everything seems good, however, the results of all concentration variables do not show any change. One thing I've noticed, the boundary conditions do not appear in the graphs as shown below especially the left ones (all of them are constants CA(0,t)=1CB(0,t)=1, CD(0,t)=2, CC(0,t)=2. I am providing my codes too.
function pdepesolver
clear;
R=1;
tend=1;
m=2;
x=linspace(0,R,2000);
t=linspace(0,tend,1000);
sol=pdepe(m, @pdepet1func,@pdepet1ic, @pdepet1BC, x, t);
A=sol(:,:,1);
B=sol(:,:,2);
D=sol(:,:,3);
C=sol(:,:,4);
figure(1)
surf(x,t,A)
title('concentration of A')
xlabel('x')
ylabel('t')
zlabel('C_A')
figure(2)
surf(x,t,B)
title('concentration of B')
xlabel('x')
ylabel('t')
zlabel('C_B')
figure(3)
surf(x,t,D)
title('concentration of D')
xlabel('x')
ylabel('t')
zlabel('C_D')
figure(4)
surf(x,t,C)
title('concentration of C')
xlabel('x')
ylabel('t')
zlabel('C_C')
function [pl, ql, pr, qr]=pdepet1BC(xl, ul, xr, ur, t)
pl=[ul(1)-1; ul(2)-1; ul(3)-2; ul(4)-2];
ql=[0; 0; 0; 0];
pr=[0;0;0;0];
qr=[1;1;1;1];
function [c,f,s]=pdepet1func(x,t,u,dudx)
DA=0.25;
DB=0.7;
DD=0.15;
DC=0.4;
muA=0.35;
muB=0.5;
muD=0.5;
c=[1; 1; 1; 1];
f=[DA*dudx(1)-(1/(muA*u(1)+muB*u(2)+4*muD*u(3)))*(muA*u(1)*DA*dudx(1)-muA*u(1)*DB*dudx(2)-2*muA*u(1)*DD*dudx(3));
DB*dudx(2)-(1/(muA*u(1)+muB*u(2)+4*muD*u(3)))*(muB*u(2)*DA*dudx(1)-muB*u(2)*DB*dudx(2)-2*muB*u(2)*DD*dudx(3));
DD*dudx(3)-(1/(muA*u(1)+muB*u(2)+4*muD*u(3)))*(2*muD*u(3)*DA*dudx(1)-2*muD*u(3)*DB*dudx(2)-4*muD*u(3)*DD*dudx(3));
DC*dudx(4)];
s=[0; 0; 0; 0];
function u0=pdepet1ic(x)
u0=[0.001;0.001;0.001;0.001];   Meteb Mejbel on 5 Jul 2021
I found the missing part. Since it's in spherical coordinates (m=2), then all left boundary conditions should be ignored which is translated to be Neumann boundary conditions.

R2019b

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