Wonky solutions for mixed parabolic-hyperbolic PDEs

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Mat Hunt 2025-7-10

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编辑： Torsten 2025-7-11

new_idea.m

I'm solving the equations:

I'm using the finite volume method with a constant spacing on dh, so it seems to be a simple solution. The boundary conditions are functions of \nu, and I compute the boundary terms by using a simple polynomial. I conpute the density which is 1/\nu, but I get funky boundary values that I don' understand. can anyone explain what is wrong?

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Mat Hunt 2025-7-11

How will that help?

The idea I used was to average over a cell, and then approximate the average by the value at the centre of the cell so I get the integrated equation:

I Then use ODE15 to solve these equations.

Torsten 2025-7-11

编辑：Torsten 2025-7-11

How will that help?

In my opinion, it helps as the first PDE becomes an ODE and to see what boundary conditions are necessary to fix a solution, namely prescribing v and vdot over [0,L] at t=0 and prescribing values that include vdot or dvdot/dh at h = 0 and h = L.

For me, your code is hard to read. Which boundary conditions do you try to impose in the formulation given ? I think this the hardest part: to know which boundary conditions are necessary and sufficient to solve this type of PDE system.

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