Linear high-resolution schemes for hyperbolic conservation laws: TVB numerical evidence

Authors:
C. Bona;C. Bona-Casas;J. Terradas
Affiliations:
Departament de Física, Universitat de les Illes Balears, Institute for Applied Computation with Community Code (IAC3), Campus Universitari, 07122 Palma de Mallorca, Spain;Departament de Física, Universitat de les Illes Balears, Institute for Applied Computation with Community Code (IAC3), Campus Universitari, 07122 Palma de Mallorca, Spain;Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

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 (TVB) 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.