1D time dependent mass transfer and reaction in a very small slab

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Moji 2018-3-29

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重新打开： Moji 2018-4-12

I am trying to model a pde including advection-diffusion and reaction terms. i want to see the concentration profil after a long time(2*60*60 sec) in a very tiny slab(5 micrometer). i used method of line(ode15s) to solve this pde but my result is not match with the experimental result. because the outlet concentration gets maximum concetration right away(as can be seen in myplot).does anybody know where is my mistake?

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John D'Errico 2018-3-29

How can someone know where your mistake might be, if you don't show the code you wrote?

Bill Greene 2018-3-31

I don't see anything wrong with your pdepe code. So I suspect there is something wrong with your constants (values or units). For example, if I make the total time 1e-7 instead of 120, the solution looks more reasonable.

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Answer 1

Abraham Boayue 2018-3-30

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By carefully defining the parameters of your function in matlab using the pdepe solver, I was able to obtain the image below. Does this look like what you want to see?

function PDEPE_diff
m = 0;
x = linspace(0,1,200);
t = linspace(0,2,100);
sol = pdepe(m,@pdepfun,@icfun,@bcfun,x,t);
u = sol(:,:,1);
plot(x,u(1:100,:,1),'linewidth',1.5)
title('Numerical solution computed with 200 mesh points.')
xlabel('Distance x')
ylabel('Time t')
grid
function [g,f,s] = pdepfun(x,t,c,DcDx)
D  = 8.6e-6;
k = 1;
K = 0.24;
ux = 0.5;
g  = 1;
f = D*DcDx;
s = -(ux*DcDx + k*K*c);
function c0 = icfun(x)
 c0 = 0*x;
   function [pl,ql,pr,qr] = bcfun(xl,cl,xr,cr,t)
  pl = cl-20;
  ql = 0;
  pr = cr;
  qr = 1;

%

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Abraham Boayue 2018-3-31

I understand what you mean. I strongly believe that it depends on the method of coding, you could try other numerical schemes like the finite difference method. Was it mentioned how the results were obtained in the paper that you are reading?

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