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Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form

Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form
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Year:    2017

Author:    Abdelaziz Beljadid, Philippe G. LeFloch, Siddhartha Mishra, Carlos Parés

Communications in Computational Physics, Vol. 21 (2017), Iss. 4 : pp. 913–946

Abstract

We propose here a class of numerical schemes for the approximation of weak solutions to nonlinear hyperbolic systems in nonconservative form – the notion of solution being understood in the sense of Dal Maso, LeFloch, and Murat (DLM). The proposed numerical method falls within LeFloch-Mishra's framework of schemes with well-controlled dissipation (WCD), recently introduced for dealing with small-scale dependent shocks. We design WCD schemes which are consistent with a given nonconservative system at arbitrarily high-order and then analyze their linear stability. We then investigate several nonconservative hyperbolic models arising in complex fluid dynamics, and we numerically demonstrate the convergence of our schemes toward physically meaningful weak solutions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2016-0019

Communications in Computational Physics, Vol. 21 (2017), Iss. 4 : pp. 913–946

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    34

Keywords:   

Author Details

Abdelaziz Beljadid

Philippe G. LeFloch

Siddhartha Mishra

Carlos Parés

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