Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws

Details Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws

2011-09-07

arxiv.org/abs/1109.1446v1

Mathematics

Numerical Analysis

22 pages, 13 figures

Scientific paper

Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating conservation laws do not take into account this fact and converge to solutions that are not necessarily physically relevant. We design numerical schemes that incorporate explicit information about the underlying viscosity mechanism and approximate the physically relevant solution. Numerical experiments illustrating the robust performance of these schemes are presented.

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