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

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-differen...

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Published in:Journal of computational physics 2009-04, Vol.228 (6), p.2266-2281
Main Authors: Bona, C., Bona-Casas, C., Terradas, J.
Format: Article
Language:English
Subjects:
Algorithms
Battery
Burgers equation
Computational techniques
Computer simulation
Exact sciences and technology
Finite difference method
Fluxes
Hyperbolic conservation laws
Mathematical analysis
Mathematical methods in physics
Mathematical models
Numerical methods
Physics
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cited_by cdi_FETCH-LOGICAL-c434t-5f55d7ec0bca3c941a6ee38ba8eadec3548872f06a078ac64c6cee4159ac4b623
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description 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.
doi_str_mv 10.1016/j.jcp.2008.12.010
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subjects Algorithms
Battery
Burgers equation
Computational techniques
Computer simulation
Exact sciences and technology
Finite difference method
Fluxes
Hyperbolic conservation laws
Mathematical analysis
Mathematical methods in physics
Mathematical models
Numerical methods
Physics
title Linear high-resolution schemes for hyperbolic conservation laws: TVB numerical evidence
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