The solution of a Riemann problem consists in determining the evolution of a fluid which is initially characterized by two uniform states with different values of density, pressure, velocity and magnetic field. Riemann solvers, either exact or approximate, are used in modern numerical codes for the solution of the equations of hydrodynamics and magnetohydrodynamics in both special and general relativity (see this review for more details).
During my PhD at SISSA I developed the first exact Riemann solver for the equations of special relativistic MHD with generic initial states. The numerical code implementing this exact solver is freely available for download and it has been used to test several numerical codes and to produce new scientific results. If you already have username and password then simply click here. Otherwise send me an email and I will give you all the information needed to download and use it.
The exact solver implements both an ideal fluid equation of state and a Synge-type EOS. Solutions obtained with the latter are described in Meliani et al 2008 A&A 491, 321-337.
Below you can find a map of some of the places where it has been used. If you see a mistake or if a place is missing, simply contact me. Thanks!
This is the list (probably incomplete) of the papers that made use of it:
- Mach P. and Piȩtka M. 2010, Exact solution of the hydrodynamical Riemann problem with nonzero tangential velocities and the ultrarelativistic equation of state, Physical Review E, 81, 046313
- Zenitani S., Hesse M. and Klimas A. 2010, Scaling of the Anomalous Boost in Relativistic Jet Boundary Layer, ApJ, 712, 951-956
- Mimica P. and Aloy M. A. 2010, On the dynamic efficiency of internal shocks in magnetized relativistic outflows, MNRAS, 401, 525-532
- Dumbser M. and Zanotti O. 2009, Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations, Journal of Computational Physics, 228, 6991–7006
- Toro E. F., Hidalgo A. and Dumbser M. 2009, FORCE schemes on unstructured meshes I: Conservative hyperbolic systems, Journal of Computational Physics, 228, 3368–3389
- Mignone A., Ugliano M. and Bodo G. 2009, A five-wave Harten-Lax-van Leer Riemann solver for relativistic magnetohydrodynamics, MNRAS, 393, 1141-1156
- Mizuno Y, Zhang B., Giacomazzo B., Nishikawa K.-I., Hardee P. E., Nagataki S. and Hartmann D. H. 2009, Magnetohydrodynamic Effects in Propagating Relativistic Jets: Reverse Shock and Magnetic Acceleration, ApJ Letters, 690, L47-L51
- Dumbser M., Balsara D. S., Toro E. F. and Muns C.-D. 2008, A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes, Journal of Computational Physics, 227, 8209–8253
- van der Holst B., Keppens R. and Meliani Z. 2008, A multidimensional grid-adaptive relativistic magnetofluid code, Computer Physics Communications, 179, 617-627
- Meliani Z., Keppens R. and Giacomazzo B. 2008, Faranoff-Riley type I jet deceleration at density discontinuities. Relativistic hydrodynamics with a realistic equation of state, A & A, 491, 321-337
- Palenzuela C., Lehner L., Reula O. and Rezzolla L. 2008, Beyond ideal MHD: towards a more realistic modeling of relativistic astrophysical plasmas, submitted to MNRAS
- Wu Y. and Cheung K.-F. 2008, Explicit solution to the exact Riemann problem and application in nonlinear shallow-water equations, International Journal for Numerical Methods in Fluids, 57, 1649-1668
- Mizuno Y., Hardee P., Hartmann D. H., Nishikawa K.-I. and Zhang B. 2008, A Magnetohydrodynamic Boost for Relativistic Jets, ApJ, 672, 72-82
- Del Zanna L., Zanotti O., Bucciantini N. and Londrillo P. 2007, ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics, A & A, 473, 11-30
- Tchekhovskoy A., McKinney J. C. and Narayan R. 2007, WHAM: a WENO-based general relativistic numerical scheme - I. Hydrodynamics, MNRAS, 379, 469-497
- Giacomazzo B. and Rezzolla L. 2007, WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics, Classical and Quantum Gravity, 24, S235-S258
- Anderson M., Hirschmann E. W., Liebling S. L. and Neilsen D. 2006, Relativistic MHD with adaptive mesh refinement, Classical and Quantum Gravity, 23, 6503-6524
- Neilsen D., Hirschmann E. W. and Millward R. S. 2006, Relativistic MHD and excision: formulation and initial tests, Classical and Quantum Gravity, 23, S505-S527
- McKinney J. C. 2006, General relativistic force-free electrodynamics: a new code and applications to black hole magnetospheres, MNRAS, 367, 1797-1807