When solving a PDE, how to assign different conductivity values to different volume regions?

Hi,

I am trying to solve an electrostatic PDE, where the electrical conductivity changes within the volume of the solution.

For example, I have a cylinder, with two electrodes at the top and bottom of the cylinder. The conductivity however changes radially within the cylinder.

My current pseudocode:

%Create PDE model
model = createpde();

sensor = importGeometry(model,modelName(ii));

figure
pdegplot(model,'FaceLabels','on');
%Apply PDE coefficients

k = 1; %k is the conductivity in S/mm, but only relevent if using neumann boundary conditions

specifyCoefficients(model,'m',0,'d',0,'c',k,'a',0,'f',0);
%Apply boundary conditions

%Positive Ring
applyBoundaryCondition(model,'dirichlet','face',[posRing1(ii)],'u',0);

%Negative Ring
%applyBoundaryCondition(model,'dirichlet','face',negRing(ii),'u',1);

Is it possible to have the k value vary for different regions? I've found a solution online for thermal diffusion problems, but instead of rewriting my whole program using the thermal analogy, I assumed there is a method for generic PDE problems.

What would be nice is if I could apply the conductivity values like how is done for the boundary conditions.

Any help is greatly appreciated.

Answer 1

[Ravi Kumar]

Hi Mark,

You sure can!

Use 'Cell' parameter in specifyCoefficients, like:

specifyCoefficients(model,'Cell',1,'m',0,'d',0,'c',k1,'a',0,'f',0);
specifyCoefficients(model,'Cell',2,'m',0,'d',0,'c',k2,'a',0,'f',0);

You can plot the geometry with Cell labels on using:

pdegplot(model,'CellLabels','on')

-Ravi

[Mark Lepage]

Thank you so much Ravi,

This is exactly what I was looking for.

Regards,

Mark

[Paul Safier]

@Ravi Kumar can you place different conductivity values for different faces of a 2D problem with the syntax: model.MaterialProperties?

[Ravi Kumar]

Hi Paul,

Yes, you can assign different conductivities to different regions using the syntax show in this example:

https://www.mathworks.com/help/pde/ug/pde.materialproperties.html#mw_2c427a0e-79df-4236-ab51-f4d2d6b78283

Note the example is for 3-D, you can do a similar assignment on faces of a 2-D model.

Regards,

Ravi