A FINITE VOLUME METHOD FOR UNDERCOMPRESSIVE SHOCK WAVES IN TWO SPACE DIMENSIONS

Christophe Chalons 1 Christian Rohde 2 Maria Wiebe 2
1 LMV - Laboratoire de Mathématiques de Versailles
2 Universität Stuttgart [Stuttgart]
Abstract : Undercompressive shock waves arise in many physical processes which involve multiple phases. We propose a Finite Volume method in two space dimensions to approximate weak solutions of systems of hyperbolic or hyperbolic-elliptic conservation laws that contain undercompressive shock waves. The method can be seen as a generalization of the spatially one-dimensional and scalar approach in [C. Chalons, P. Engel and C. Rohde, SIAM J. Numer. Anal. 52 (2014) 554-579]. It relies on a moving mesh ansatz such that the undercompressive wave is represented as a sharp interface without any artificial smearing. It is proven that the method is locally conservative and recovers planar traveling wave solutions exactly. To demonstrate the efficiency and reliability of the new scheme we test it on scalar model problems and as an application on compressible liquid-vapour flow in two space dimensions.
Keywords : Undercompressive shock waves in 2D hyperbolic-elliptic systems interface tracking Finite Volume method
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Journal articles
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Submitted on : Monday, July 1, 2019 - 11:36:46 AM
Last modification on : Friday, January 10, 2020 - 3:42:28 PM

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Christophe Chalons, Christian Rohde, Maria Wiebe. A FINITE VOLUME METHOD FOR UNDERCOMPRESSIVE SHOCK WAVES IN TWO SPACE DIMENSIONS. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2017, 51 (5), pp.1987-2015. ⟨10.1051/m2an/2017027⟩. ⟨hal-02169453⟩

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