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A Conservative Method for the Simulation of the Isothermal Euler System with the van-der-Waals Equation of State

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Abstract

In this article, we are interested in the simulation of phase transition in compressible flows, with the isothermal Euler system, closed by the van-der-Waals model. We formulate the problem as an hyperbolic system, with a source term located at the interface between liquid and vapour. The numerical scheme is based on (Abgrall and Saurel, J. Comput. Phys. 186(2):361–396, 2003; Le Métayer et al., J. Comput. Phys. 205(2):567–610, 2005). Compared with previous discretizations of the van-der-Waals system, the novelty of this algorithm is that it is fully conservative. Its Godunov-type formulation allows an easy implementation on multi-dimensional unstructured meshes.

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  1. Laboratoire de Mathématiques et de leurs Applications, INRIA Bordeaux Sud-Ouest, Avenue de l’Université, 64000, Pau, France

    Vincent Perrier

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  1. Vincent Perrier
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Correspondence to Vincent Perrier.

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Perrier, V. A Conservative Method for the Simulation of the Isothermal Euler System with the van-der-Waals Equation of State. J Sci Comput 48, 296–303 (2011). https://doi.org/10.1007/s10915-010-9415-9

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  • DOI: https://doi.org/10.1007/s10915-010-9415-9

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