Piecewise Parabolic Method (PPM)


Astronomy research
Software instruments
   Stellar equation of states
   EOS with ionization
   EOS for supernovae
   Chemical potentials
   Stellar atmospheres

   Voigt Function
   Jeans escape
   Polytropic stars
   Cold white dwarfs
   Hotter white dwarfs

   Cold neutron stars
   Stellar opacities
   Neutrino energy loss rates
   Ephemeris routines
   Fermi-Dirac functions

   Galactic chemical evolution
   Coating an ellipsoid
   Universal two-body problem

   Nuclear reaction networks
   Nuclear statistical equilibrium
   Laminar deflagrations
   CJ detonations
   ZND detonations

   Fitting to conic sections
   Unusual linear algebra
   Derivatives on uneven grids
   Pentadiagonal solver
   Quadratics, Cubics, Quartics

   Supernova light curves
   Exact Riemann solutions
   1D PPM hydrodynamics
   Verification problems
   Plane - cube Intersection

   The pendulum
   Circular and elliptical 3 body


   Zingale's software
   Brown's dStar
   GR1D code
   Iliadis' STARLIB database
   Herwig's NuGRID
   Meyer's NetNuc
Bicycle adventures

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2019 JINA R-process Workshop
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Teaching materials
Education and Public Outreach

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.