How can I simulate 2 materials in pde toolbox script?

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Laura Pare 2016-9-8

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回答： Moncef 2019-7-1

In order to simulate 2 materials in a heat diffusion equation I define 2 different geometries, but then how I define the different coefficients for each material? One has heat source and the other hasn't. I am doing it as shown bellow, but the results are not what I would expect, so I am wondering if I am doing it right. There is another way to do that? Do I need to define 2 diff. equations instead?

Thank you very much in advance,

Here is my script:

numberOfPDE = 1;
model = createpde(numberOfPDE);
r1 = [3,4,0,0,0.5*10^-6,0.5*10^-6,-160*10^-9,-1.16*10^-6,-1.16*10^-6,-160*10^-9];
r2 = [3,4,0,0,0.5*10^-6,0.5*10^-6,0,-160*10^-9,-160*10^-9,0];
gdm = [r1; r2]';
g = decsg(gdm,'R1+R2',['R1'; 'R2']');
geometryFromEdges(model,g);
specifyCoefficients(model,'m',0,'d',5,'c',16,'a',0,'f',0,'face',1);
specifyCoefficients(model,'m',0,'d',5,'c',50,'a',0,'f',2*10^18,'face',2);
applyBoundaryCondition(model,'edge',1,'r',298);
applyBoundaryCondition(model,'edge',2,'q',2000,'g',596000);
applyBoundaryCondition(model,'edge',3,'g',0);
applyBoundaryCondition(model,'edge',4,'g',0);
applyBoundaryCondition(model,'edge',6,'g',0);
applyBoundaryCondition(model,'edge',7,'g',0);
hmax = 2*10^-8; % element size
msh=generateMesh(model,'Hmax',hmax);
tinitial = 0;
tfinal = 2*10^-8;
interval = 100;
tlist = linspace(tinitial,tfinal,interval);
u0 = 298; % initial temperature in the geometry 
setInitialConditions(model,u0);
results = solvepde(model,tlist);
u = result.NodalSolution;
%Plot the solution at time t = tfinal.
figure;
pdeplot(model,'xydata',results.NodalSolution,'contour','on')

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michio 2016-9-8

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It seems to me that you are doing alright in specifying different coefficients for different sub-domains. I assume two different materials are represented by the two sub-domains.

specifyCoefficients(model,'m',0,'d',5,'c',16,'a',0,'f',0,'face',1);
specifyCoefficients(model,'m',0,'d',5,'c',50,'a',0,'f',2*10^18,'face',2);

It may help us help you if you describe more about your issues, your problem settings, what part of the result is not what you expect.

Laura Monreal 2016-9-14

Hi Michio,

I changed my name because I had problems with the other sesion. Thank you for you answer. So, in fact my f coefficient for the subdomain 2 is a cosinus that I do not see in the simulation, but i see it when I simulatet the "material" 2 byitself. I think I am not getting the result I spect because of the mesh, there is a way to introduce different meshing for different subdomains? I saw that you can not implement refinemesh usind a PDEmodel, so how should I do it?

Thank you in advance

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Answer 1

michio 2016-9-14

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编辑：michio 2016-9-15

Thanks for your clarification. As you have already made use of it, but sub-domain support is available for 2D problems, so yes you can simulate 2 materials using PDE Toolbox.

If your issue is really caused by meshing, you can try legacy workflow that supports refinement. This entry might be of your help. How can I refine a subdomain in the PDE Toolbox mesh generation tool?

I didn't understand the details since you mentioned "my f coefficient for the subdomain 2 is a cosinus". If your f coefficient needs to be expressed as some function of space, you can try defining f coefficient in a functional form. The related doc page is f Coefficient for specifyCoefficients

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Laura Pare 2016-9-16

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Hi Michio,

Thank you very much for your answer. It was very helpful, I am doing it in the legacy workflow and even without refining the mesh differently for the different subdomains I see results that make much more sense to me. But the only thing I don't know how to do now is to express a constant coeffitient for different subdomains.

I have this:

u = parabolic(u0,tlist,model,'ccoeff(sd)',a,f,'dcoeff(x,y,t,u,sd)');

And the d is function like that:

if true
function d = dcoeff(x,y,t,u,sd)
d = 3950*(92.4+3.8*10^(-2).*(u)-2.2*10^6.*(u).^(-2))/101.9612*1000; % d on subdomain 1 (znO)
r = '(sd == 2)'; % subdomain 2
d2 = 5600*(47.8+6.1*10.^(-3)*(u)-7.6*10^5.*(u).^(-2))/81.3794*1000; % coefficient on subdomain 2 (Alumina)
d(r) = d2(r); % d on subdomain 2
end

But the c coeffitient is constant in both subdomains but differwent between them. I write this, but it tell me Index exceeds matrix dimensions.In expression: ccoeff(sd) when evaluating pde coefficients.

if true
function c = ccoeff(sd)
c = 50; % d on subdomain 1 
r = '(sd == 2)'; % subdomain 2
c2 = 16; % coefficient on subdomain 2 
c(r) = c2(r); % d on subdomain 2
end