Hello everyone,
I am trying to solve a heat diffusion problem in a regressing cylinder and found an obstacle in modelling the moving boundary conditions. The equation I am using is:
du/dt = k * d2u/dx2 + dr(t) * du/dx
where dr(t) is the regression velocity of the internal wall of the cylinder and is given at any time.
So far the only thing I could come up with was to do a for cycle; for each time step I solve the PDE (pdepe with m=1) and after that I use the just found solution as the initial condition for the new cycle, all this to allow me to change the space mesh at each cycle. I understand that this is not the right way to do it (if I understand correctly I'm practically turning the PDE into an ODE) but I tried and got decent results.
Nonetheless I would like to find a better way to simulate the material regression. Any help is appreciated, sorry for any technical mistakes, I am kind of new to all this as still learning!
