MethodOfLines.jl
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add Piecewise Parabolic Method discretization method
Reference: https://www.sciencedirect.com/science/article/pii/0021999184901438?via%3Dihub
Currently tests/demo_ppm_runs.jl
shows that it's usable as a substitute for WENO, and tests/demo_parker_singular.jl
shows that it can create a SingularException
that I'd like to try and chase down.
PPM is explicitly dependent on the timestep, so only fixed-timestep methods should be used. I think the best ones are forward/implicit Euler, since that's what past astro codes that use PPM have used.
PPM is also compatible with varying dx, which I'd like to try out with the Parker wind problem (which has a logarithmic x axis that I analytically transformed to be uniform) once the fixed-dx case works.