Using PDEPE to model a hollow cylinder?
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I'm trying to model a chemical reaction within the thick wall of a long hollow cylinder. It is a 1D (x,t) PDE as a linked system of 2 or 3 parameters (temperature, reaction state, maybe pressure) with a heat transfer boundary condition on the inner or outer wall (and possibly both) and heat release within the material (which is porous and reacting with a gas).
I was meaning to use PDEPE but I see from the documentation that for intervals a<x<b that one can only set conditions at x=a or x=b, not both, and also that for a cylinderical geometry the solver only models solid cylinders with a=0.
is this correct? Is there a work-around or should I take a Method of Lines approach and use ODE45 instead? Or code my own solver from scratch?
Also, if I were able to use PDEPE, how could the function that sets [c, f, s] sum at the whole-mesh values of x to determine the system pressure? I've looked at the documentation example and this function seems to be called with scalar arguments, for one node at a time.
Thanks
Roger
3 Comments
Bill Greene
on 26 Aug 2020
If and , then the mathematics requires a symmetry condition at the center; pdepe is just sort of helping you out there. Since you have , that doesn't apply.
Beyond that, I suggest you edit your equation to include your equations along with boundary and initial conditions.
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