We consider the approximation of entropy solutions to nonlinear hyperbolic conservation laws, in the regime that small–scale effects drive the dynamics of shock waves in these solutions. We introduce and analyze a new class of numerical methods, referred to as the schemes with well-controled dissipation (WCD), which approximate entropy solutions with high–accuracy and can capture small scale dependent shock waves of arbitrary strength. Following earlier work by LeFloch and collaborators, we rely on the equivalent equation associated with a finite difference scheme which provides us with the proper tool in order to ensure that small-scale dependent shock waves are computed accurately. Examples involving nonclassical shocks for cubic conservation laws, the nonlinear elasticity system, and a reduced model of magnetohydrodynamics are investigated with our approach. Show more
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Journal / seriesResearch Report
PublisherSAM, ETH Zürich
Organisational unit03851 - Mishra, Siddhartha / Mishra, Siddhartha
NotesSee also: http://e-citations.ethbib.ethz.ch/view/pub:158609.
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