The limiting behavior of the compressible two-phase flow models for turbulent mixing is discussed near the initial time as the Mach number tends to zero. We examine transitional variables in the closed form and the unknown boundary data by proper matching conditions. The inner limit asymptotics are determined in the fast-transition layers.

zero Mach number limit, singular perturbation, two-phase flow, asymptotic expansions, turbulent mixing

Received: May 15, 2024; Accepted: June 24, 2024; Published: August 5, 2024

How to cite this article: Hyeonseong Jin, The asymptotics of slightly compressible two-phase flow equations in the fast-transition layers, JP Journal of Heat and Mass Transfer 37(4) (2024), 457-469. https://doi.org/10.17654/0973576324032

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

References:
[1] 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.
[2] D. Ebin, Motion of slightly compressible fluids in a bounded domain I, Comm. Pure Appl. Math. 35 (1982), 451-485.
[3] J. Glimm and H. Jin, An asymptotic analysis of two-phase fluid mixing, Bol. Soc. Bras. Mat. 32 (2001), 213-236.
[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, Fast transition layers of weakly compressible two phase flow equations near initial time, Global J. Pure Appl. Math. 13(2) (2017), 627-645.
[9] H. Jin, Perturbative approach to weakly compressible multiphase flow, JP J. Heat Mass Transf. 15(4) (2018), 983-1001.
[10] H. Jin, Asymptotics of the volume fractions for low Mach number multiphase flow equations, JP J. Heat. Mass Transf. 22(1) (2021), 107-122.
[11] H. Jin, Matching of spatially uniform asymptotic solutions of weakly compressible multiphase flow equations, 2024 (in preparation).
[12] H. Jin and J. Glimm, Weakly compressible two-pressure two-phase flow, Acta Math. Sci. Ser. B (Engl. Ed.) 29(6) (2009), 1497-1540.
[13] H. Jin, J. Glimm and D. H. Sharp, Compressible two-pressure two-phase flow models, Phys. Lett. A. 353 (2006), 469-474.
[14] J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1985.
[15] 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.
[16] H.-O. Kreiss and J. Lorenz, Initial-boundary Value Problems and the Navier Stokes Equations, Academic Press, Inc., 1989.
[17] H. Lee, H. Jin, Y. Yu and J. Glimm, On the validation of turbulent mixing simulations of Rayleigh-Taylor mixing, Phys. Fluids 20 (2008), 012102.