We study the limiting motion of low Mach number two-phase flow equations near initial time. Under the layer-type singular limit process, matching conditions are clarified to derive the spatially uniform asymptotics of compressible solutions. We examine the unknown boundary data and transitional variables in closed form.

singular perturbation, two-phase flow, asymptotic expansions.

Received: April 17, 2022; Revised: May 30, 2022; Accepted: June 20, 2022; Published: July 15, 2022

How to cite this article: Hyeonseong Jin, The limiting motion of low Mach number two-phase flow, JP Journal of Heat and Mass Transfer 28 (2022), 61-70. http://dx.doi.org/10.17654/0973576322034

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] W. Bo, H. Jin, D. Kim, X, Liu, H. Lee, N. Pestieau, Y. Yu, J. Glimm and J. Grove, Comparison and validation of multiphase closure models, Comput. Math. Appl. 56 (2008), 1291-1302.
[2] Y. Chen, J. Glimm, D. H. Sharp and Q. Zhang, A two-phase flow model of the Rayleigh-Taylor mixing zone, Phys. Fluids 8(3) (1996), 816-825.
[3] D. Ebin, Motion of slightly compressible fluids in a bounded domain I, Comm. Pure Appl. Math. 35 (1982), 451-485.
[4] J. Glimm, H. Jin, M. Laforest, F. Tangerman and Y. Zhang, A two pressure numerical model of two fluid mixtures, SIAM J. Multiscale Modeling and Simulation 1 (2003), 458-484.
[5] J. Glimm, D. Saltz and D. H. Sharp, Two-pressure two-phase flow, Nonlinear Partial Differential Equations, G.-Q. Chen, Y. Li and X. Zhu, eds., World Scientific, Singapore, 1998.
[6] J. Glimm, D. Saltz and D. H. Sharp, Two-phase modeling of a fluid mixing layer, J. Fluid Mech. 378 (1999), 119-143.
[7] D. Hoff, The zero-mach limit of compressible flows, Commun. Math. Phys. 192 (1998), 543-554.
[8] H. Jin, The inner limit process of slightly compressible multiphase equations, Glob. J. Pure Appl. Math. 12(3) (2016), 2219-2241.
[9] H. Jin, Phase transitions in the zero Mach number limit of compressible twophase flow equations, JP Journal of Heat and Mass Transfer 16(2) (2019), 351-386.
[10] H. Jin and J. Glimm, Weakly compressible two-pressure two-phase flow, Acta Math. Sci. Ser. B (Engl. Ed.) 29(6) (2009), 1497-1540.
[11] J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1985.
[12] S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math. 34 (1981), 481-524.