A mixture-energy-consistent numerical approximation of a two-phase flow model for fluids with interfaces and cavitation

Abstract : We model cavitating flows by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas– Berry [J. Comput. Phys. 228, 1678 (2009)]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure with the correct mixture equation of state. The two-phase system is solved in two dimensions by a fully-discretized high-resolution wave propagation scheme based on a HLLC/Roe Riemann solver. Numerical experiments show the ability of the numerical model to describe mechanical cavitation processes.
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F. Ancona, A. Bressan, P. Marcati, A. Marson. 14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2012), Jun 2012, Padova, Italy. AIMS (American Institute of Mathematical Sciences), pp.839-846, 2014, Hyperbolic Problems: Theory, Numerics, Application. 〈http://www.hyp2012.eu/〉
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Marica Pelanti, Keh-Ming Shyue. A mixture-energy-consistent numerical approximation of a two-phase flow model for fluids with interfaces and cavitation. F. Ancona, A. Bressan, P. Marcati, A. Marson. 14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2012), Jun 2012, Padova, Italy. AIMS (American Institute of Mathematical Sciences), pp.839-846, 2014, Hyperbolic Problems: Theory, Numerics, Application. 〈http://www.hyp2012.eu/〉. 〈hal-01136009〉

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