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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Abgrall, R., Saurel, R.: Discrete equations for physical and numerical compressible multiphase mixtures. J. Comput. Phys. 186(2), 361–396 (2003)
Drew, D.A., Passman, S.L.: Theory of Multicomponent Fluids. Applied Mathematical Sciences, vol. 135. Springer, New York (1999)
Hou, T.Y., LeFloch, P.G.: Why nonconservative schemes converge to wrong solutions: error analysis. Math. Comput. 62(206), 497–530 (1994)
Jamet, D., Lebaigue, O., Coutris, N., Delhaye, J.M.: The second gradient method for the direct numerical simulation of liquid-vapor flows with phase change. J. Comput. Phys. 169(2), 624–651 (2001)
Le Métayer, O., Massoni, J., Saurel, R.: Modelling evaporation fronts with reactive Riemann solvers. J. Comput. Phys. 205(2), 567–610 (2005)
LeFloch, P.: Propagating phase boundaries: formulation of the problem and existence via the Glimm method. Arch. Ration. Mech. Anal. 123(2), 153–197 (1993)
Merkle, C., Rohde, C.: The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques. M2AN Math. Model. Numer. Anal. 41(6), 1089–1123 (2007)
Serre, D.: Systems of Conservation Laws (1 & 2). Cambridge University Press, Cambridge (1999)
Slemrod, M.: Admissibility criteria for propagating phase boundaries in a van der Waals fluid. Arch. Ration. Mech. Anal. 81(4), 301–315 (1983)
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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