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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Bona, C.¹  Bona-Casas, C.¹  Terradas, J.² 

[1] Univ Illes Balears, Dept Fis, Inst Appl Computat Community Code IAC3, Palma de Mallorca 07122, Spain

[2] Katholieke Univ Leuven, Ctr Plasma Astrophys, B-3001 Louvain, Belgium

关键词: Hyperbolic conservation laws;    Numerical methods;   

DOI  :  10.1016/j.jcp.2008.12.010

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free