Diffusion equation in Cartesian and Cylindrical coordinates

Hi Matlab Team,

I have written the code for the diffusion equation in Cartesian and Cylindrical coordinates using pdepe. However, in cylindrical coordinate, the graph is to the left and it is not symmetric. I think it is becasue of the geometry of cylindrical coordinate, but how can I fixed it to have a similar graph from cartesian and cylindrical code?

Thanks

[Torsten]

Your description is far too vague to be able to give advice.

We need your code to reproduce what you are talking about.

[Neda]

@Torsten

Thank you !! Here is my code: when I change m from 0 to 1, the solution changes.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

m = 0;

x = linspace(0,1,201);

t = linspace(0,5,101);

sol = pdepe(m,@diffusion,@diffic,@diffbc,x,t);

u = sol;

surf(x,t,u)

%--------------------------------------------------------------------------

figure

for t_num = 1:length(t)

%----------------------------------------------------------------------

% Plot figure

hold off

plot(x, sol(t_num,:))

hold on

v = axis;

axis([x(1) x(end) 0 1])

getframe;

end

%--------------------------------------------------------------------------

% PDE function

function [c,f,s] = diffusion(x,t,u,dudx)

D = 0.01;

mu = 0.1;

K = 20;

c = 1;

f = (D)*dudx ;

s = 0;

end

% initial condition

function u0 = diffic(x)

% u0 = 0;

u0 = 0.01 + 0.99*(0.4 <= x)*(x <= 0.6);

end

% local function 3

function [pl,ql,pr,qr] = diffbc(xl,ul,xr,ur,t)

F = 0.0005;

pl = F; %

ql = 1; %

pr = 0; %

qr = 1; %

end

Answer 1

[Torsten]

If m = 1, the condition at r = 0 set by "pdepe" is pl = 0, ql = 1. All other conditions make no sense mathematically because they would cause an unbounded solution for u at r = 0. So your setting pl = F will be internally overwritten by the solver.

Further, I don't understand why you are suprised that the solution changes when you change m from 0 to 1. Of course it will change because diffusion in a cylinder in r-direction differs from diffusion in a plate. Since the areas through which diffusion takes place are smaller in the region from 0 to 0.4 than from 0.6 to 1, concentration will increase faster in the region from 0 to 0.4 than from 0.6 to 1 - the profiles loose their symmetry.