Facing problem to solve convection-diffusion equation
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I want to solve simple diffusion equation MATLAB.
(del_C/del_t)=(D^2)(del^2_C/del_x^2)-U(del_C/del_x)
I.C: C(x,0)=C0; B.C: C(0,t)=C0, C(L,t)=C1
My program:
numr =50; %number of grid points in x direction
numt = 10000; %number of time steps
L = 0.01; %thickness of a flat plate (m)
dx = R/(numr - 1); %grid size in x direction
dt = 0.0005;
D = 1.0e-05; %species diffusivity
C0 = 1.0; %species initial concentration
Cinf = 0.1; %species surface concentration
x = 0:dx:L; %vector of x positions
C = zeros(numr,numt); %initialize the concentration C(x,t) matrix
%specify initial conditions along the radius(C=C0,x=0 to L,t=0)
t(1) = 0;
for i=1:numr
C(i,1)=C0;
end
% uniform boundary condition at the centre(C=C0,x=0,t=0 to tf)constant mass
% source term
for j = 1:numt
C(1,j)=C0;
end
% boundary condition at particle surface (C=Cinf,x=L,t>0)
% specis concentration is fixed at the boundary
for j=2:numt
C(numr,j)=Cinf;
end
%Stability criteria
%dx<(2*D)/u
%dt<(dx^2)/(2*D)
u=0.5;
s=D*dt/(2*dx^2);
p=u*dt/(4*dx);
%iteration based on forward differencing scheme
for j=2:numt
t(j) = t(j-1) + dt;
for i=2:numr-1
C(i,j+1)=C(i,j)+(s-p)*(C(i+1,j+1)+C(i+1,j))-(2.0*s)*(C(i,j+1)+C(i,j))+(s+p)*(C(i-1,j+1)+C(i-1,j));
end
end
plot(C,x)
xlabel('x direction')
ylabel('C')
采纳的回答
Walter Roberson
2018-6-28
Your line
C(i,j+1)=C(i,j)+(((s-p)*C(i+1,j+1)+(s-p)*C(i+1,j)+((-2*s)*C(i,j+1))+((-2*s)*C(i,j))+((s+p)*C(i-1,j+1))+((s+p)*C(i-1,j));
is missing two closing brackets somewhere
C(i,j+1)=C(i,j)+(((s-p)*C(i+1,j+1)+(s-p)*C(i+1,j)+((-2*s)*C(i,j+1))+((-2*s)*C(i,j))+((s+p)*C(i-1,j+1))+((s+p)*C(i-1,j));
1 0 1 0 123 2 3 2 3 2 3 2 34 3 4 32 34 3 4 32 34 3 4 32 34 3 4 32
so at the end of the expression you have 2 unclosed brackets.
3 个评论
Raj001
2018-6-28
Walter Roberson
2018-6-28
Difficult for me to check without knowing the correct code.
Raj001
2018-6-28
更多回答（1 个）
Torsten
2018-6-28
On the right-hand side of the equation
C(i,j+1)=C(i,j)+(((s-p)*C(i+1,j+1)+(s-p)*C(i+1,j)...
you refer to elements C(.,j+1) that are not yet known. This is the general problem.
The "index exceeds matrix dimensions" error is caused by this reference to C(i,j+1) for j=numt since you allocated C as C=zeros(numr,numt).
Best wishes
Torsten.
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