Low Mach number limit of a diffuse interface model for two-phase flows of compressible viscous fluids

被引：0

作者：

Abels, Helmut ^{[1
]}

Liu, Yadong ^{[2
]}

Nečasová, Šárka ^{[3
]}

机构：

[1] Fakultät für Mathematik, Universität Regensburg, Regensburg

[2] School of Mathematical Sciences, Nanjing Normal University, Nanjing

[3] Institute of Mathematics, Czech Academy of Sciences, Praha

来源：

GAMM Mitteilungen | 2024年 / 47卷 / 04期

关键词：

Cahn–Hilliard; diffuse interface model; low Mach number limit; Navier–Stokes; two-phase flow;

D O I：

10.1002/gamm.202470008

中图分类号：

学科分类号：

摘要：

In this paper, we consider a singular limit problem for a diffuse interface model for two immiscible compressible viscous fluids. Via a relative entropy method, we obtain a convergence result for the low Mach number limit to a corresponding system for incompressible fluids in the case of well-prepared initial data and same densities in the limit. © 2024 The Authors. GAMM-Mitteilungen published by Wiley-VCH GmbH.

引用

共 36 条

[1]

Abels H., On a diffuse interface model for two-phase flows of viscous, incompressible fluids with matched densities, Arch. Rat. Mech. Anal., 194, pp. 463-506, (2009)

[2]

Abels H., Feireisl E., On a diffuse interface model for a two-phase flow of compressible viscous fluids, Indiana Univ. Math. J., 57, pp. 659-698, (2008)

[3]

Abels H., Garcke H., Giorgini A., Global regularity and asymptotic stabilization for the incompressible Navier–stokes-Cahn–Hilliard model with unmatched densities, Math. Ann., 389, pp. 1267-1321, (2024)

[4]

Anderson D.M., McFadden G.B., Wheeler A.A., Diffuse-interface methods in fluid mechanics, Annual review of fluid mechanics, 30, pp. 139-165, (1998)

[5]

Boyer F., Mathematical study of multi-phase flow under shear through order parameter formulation, Asymptot. Anal., 20, pp. 175-212, (1999)

[6]

Cherfils L., Feireisl E., Michalek M., Miranville A., Petcu M., Prazak D., The compressible Navier-stokes-Cahn-Hilliard equations with dynamic boundary conditions, Math. Models Methods Appl. Sci., 29, pp. 2557-2584, (2019)

[7]

Dafermos C.M., The second law of thermodynamics and stability, Arch. Ration. Mech. Anal., 70, pp. 167-179, (1979)

[8]

Danchin R., Zero mach number limit for compressible flows with periodic boundary conditions, Am. J. Math., 124, pp. 1153-1219, (2002)

[9]

Desjardins B., Grenier E., Low Mach number limit of viscous compressible flows in the whole space, R Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 455, pp. 2271-2279, (1999)

[10]

Desjardins B., Grenier E., Lions P.-L., Masmoudi N., Incompressible limit for solutions of the isentropic Navier-stokes equations with Dirichlet boundary conditions, J. Math. Pures Appl, 78, 9, pp. 461-471, (1999)

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