Applications of Mathematics, Vol. 68, No. 4, pp. 467-483, 2023
An entropy stable finite volume method for a compressible two phase model
Eduard Feireisl, Mădălina Petcu, Bangwei She
Received February 20, 2022. Published online March 29, 2023.
Abstract: We study a binary mixture of compressible viscous fluids modelled by the Navier-Stokes-Allen-Cahn system with isentropic or ideal gas law. We propose a finite volume method for the approximation of the system based on upwinding and artificial diffusion approaches. We prove the entropy stability of the numerical method and present several numerical experiments to support the theory.
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Affiliations: Eduard Feireisl, Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic, e-mail: feireisl@math.cas.cz; Mădălina Petcu, Laboratoire de Mathématiques et Applications, UMR CNRS 7348-SP2MI, Université de Poitiers, Boulevard Marie et Pierre Curie-Téléport 2, 86962 Chasseneuil, Futuroscope Cedex, France; The Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania; The Institute of Statistics and Applied Mathematics of the Romanian Academy, Calea Victoriei 125, Sector 1, Cod 010071, Bucharest, Romania; e-mail: madalina.petcu@math.univ-poitiers.fr; Bangwei She (corresponding author), Academy for Multidisciplinary Studies, Capital Normal University, West 3rd Ring North Road 105, 100048 Beijing, P. R. China; Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic, e-mail: she@math.cas.cz
