Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-10-13
J.Comput.Phys.228:2266-2281,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Revised version, including new tests to appear in Journal of Computational Physics
Scientific paper
10.1016/j.jcp.2008.12.010
The Osher-Chakrabarthy family of linear flux-modification schemes is considered. Improved lower bounds on the compression factors are provided, which suggest the viability of using the unlimited version. The LLF flux formula is combined with these schemes in order to obtain efficient finite-difference algorithms. The resulting schemes are applied to a battery of numerical tests, going from advection and Burgers equations to Euler and MHD equations, including the double Mach reflection and the Orszag-Tang 2D vortex problem. Total-variation-bounded behavior is evident in all cases, even with time-independent upper bounds. The proposed schemes, however, do not deal properly with compound shocks, arising from non-convex fluxes, as shown by Buckley-Leverett test simulations.
Bona Carles
Bona-Casas Carles
Terradas Jaume
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