A robust entropy-satisfying finite volume scheme for the isentropic Baer-Nunziato model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 1, p. 165-206
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We construct an approximate Riemann solver for the isentropic Baer-Nunziato two-phase flow model, that is able to cope with arbitrarily small values of the statistical phase fractions. The solver relies on a relaxation approximation of the model for which the Riemann problem is exactly solved for subsonic relative speeds. In an original manner, the Riemann solutions to the linearly degenerate relaxation system are allowed to dissipate the total energy in the vanishing phase regimes, thereby enforcing the robustness and stability of the method in the limits of small phase fractions. The scheme is proved to satisfy a discrete entropy inequality and to preserve positive values of the statistical fractions and densities. The numerical simulations show a much higher precision and a more reduced computational cost (for comparable accuracy) than standard numerical schemes used in the nuclear industry. Finally, two test-cases assess the good behavior of the scheme when approximating vanishing phase solutions.

DOI : https://doi.org/10.1051/m2an/2013101
Classification:  76T05,  35L60,  35F55
Keywords: two-phase flows, entropy-satisfying methods, relaxation techniques, Riemann problem
     author = {Coquel, Fr\'ed\'eric and H\'erard, Jean-Marc and Saleh, Khaled and Seguin, Nicolas},
     title = {A robust entropy-satisfying finite volume scheme for the isentropic Baer-Nunziato model},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {1},
     year = {2014},
     pages = {165-206},
     doi = {10.1051/m2an/2013101},
     zbl = {1286.76098},
     mrnumber = {3177841},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_1_165_0}
Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled; Seguin, Nicolas. A robust entropy-satisfying finite volume scheme for the isentropic Baer-Nunziato model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 1, pp. 165-206. doi : 10.1051/m2an/2013101. http://www.numdam.org/item/M2AN_2014__48_1_165_0/

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