Geodesic
An entropy stable finite volume method for a compressible two phase model
Applications of Mathematics, Tome 68 (2023) no. 4, pp. 467-483.

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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.
DOI : 10.21136/AM.2023.0041-22
Classification : 65M12, 76N06, 76Txx
Keywords: compressible Navier-Stokes-Allen-Cahn; finite volume method; entropy stability 
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Feireisl, Eduard; Petcu, Mădălina; She, Bangwei. An entropy stable finite volume method for a compressible two phase model. Applications of Mathematics, Tome 68 (2023) no. 4, pp. 467-483. doi : 10.21136/AM.2023.0041-22. http://geodesic.mathdoc.fr/articles/10.21136/AM.2023.0041-22/

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