Exact Riemann Solver


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

AAS Journals
2019 JINA R-process Workshop
2019 MESA Marketplace
2019 MESA Summer School
2019 AST111 Earned Admission
Teaching materials
Education and Public Outreach

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

The code exact_riemann.f solves the riemann problem of a discontinuity across an interface, and in its original form is from Bruce Fryxell. While the Sod problem has become a standard hydrodynamic test case, it isn't a very discriminating test for modern software instruments. The strong shock tube problem below is more demanding because of the stronger discontinuities across the shock interface and the narrow density peak that forms behind the shock. The γ=1.4 test case shown below sets the time=0 density to ρ(x < 2)=10 and ρ(x > 2)=1, and the time=0 pressure to P(x < 2)=100 and P(x >2)=1. The exact Riemann solution at 0.4 s is (click image to see a pdf version)


If you want a simple 1D hydrodynamics code, check out this PPM code. If you want a reasonably modern hydrodynamics code, check out The FLASH code. Mike Zingale's software page offers several open-source hydro codes for research and teaching.

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.