Moving boundary conditions (material regressions) for PDE
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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!
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Torsten
el 11 de Nov. de 2022
Editada: Torsten
el 11 de Nov. de 2022
Your equation
du/dt = k * d2u/dx2 + dr/dt * du/dx
seems to be written in cartesian, not in cylindrical coordinates.
The usual way to solve moving boundary problems is to introduce dimensionless variables
r~ = r / R(t)
rewrite the equation in r~ and solve the transformed equation over the fixed interval [0 1] for r~.
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