I am solving a PDE to simulate current flow through a conductive medium in 2D.
My geometry is as follows:
With Neumann boundary conditions applied to edges E2 and E4, like so:
I am only interested in solving the PDE in the form of the Laplace equation:
, where is electric potential (which we are solving for) and σ is the conductivity tensor, which is represented as the c coefficient in our PDE model.
I want to apply a time-dependent c coefficient to the subdomain, F2, whereby the conductivity changes in time such that c = t/(t+constant).
I have tried the following lines of code:
c1 = [1;0;0;1];
c2 = @(location,state)(repmat([1;0;0;1].*state.time./(state.time + 1),1,length(location.x)));
However, I am unsure about how to specify the time scale as the rest of the PDE is time-independent. I have found that
tlist = 0:0.01:1;
results = solvepde(model,tlist);
does not work.
Any help is appreciated.
Additional, but less urgent:
Once this step is completed, I aim to have the conductivity tensor also non-constant in x and y, so that it has something resembling a normal distribution (smallest conductivity in the centre of Face 2 and parabolically tending towards equilibrium at the edges. If anyone has any ideas on how to tackle this, that would be great.