Piecewise Parabolic Method (PPM)


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   The pendulum


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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.

The tool in the bzip2 tar file ppm1d.tbz, originally written by Bruce Fryxell, is a 1D PPM hydrodynamics solver on Cartesian grids. It has the advantage of being small and self-contained in a single file. If you want a tool with more capability (e.g, 1D spherical grids or explicit equation of state calls) then check out Mike Zingale's hydro1d github project - its very nice.

While the Sod problem has become a standard test case for hydrodynamics instruments it isn't a very discriminating test for modern software instruments. The strong shock tube problem below is a more demanding test problem, because of the stronger discontinuities across the shock interface and the narrow density peak that forms behind the shock. The tool sets the initial density to 10 on the left, and 1 on the right. The initial pressure is set to 100 on the left, and 1 on the right. The PPM solution and the exact solution to the exact Riemann solution at 0.4 s is compared below.

Time Evolution
Final Pressure profile
Final Density profile
Final Velocity profile

If you want a simple exact Riemann solver, check out this page. If you want a modern multi-physics, multi-scale, multi-dimensional hydrodynamics instrument, check out FLASH, CASTRO, or MAESTO.

Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.