Far Eastern Mathematical Journal

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Numerical modeling of the Rayleigh-Taylor instability using multiphase model


Vasiliev A.E.

2025, issue 2, P. 194–210
DOI: https://doi.org/10.47910/FEMJ202513


Abstract
The article presents research on the applicability of the Baer-Nunziato type multiphase systems to the numerical modeling of the Rayleigh-Taylor instability in metals under extreme «pseudo-liquid» conditions. A model problem with a sinusoidal disturbance of the contact boundary between metals is considered. The results show compliance with theoretical estimates. A study of the influence of compressibility on the development of the process was conducted. The results obtained indicate the influence of phase compressibility not only on the process itself, but also on the features of its numerical modeling.

Keywords:
numerical modeling, multiphase flow, Rayleigh-Taylor instability, Baer-Nunziato equations, HLLC solver.

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References

[1] Godunov S., Deribas A., Zabrodin A., Kozin N., “Hydrodynamic effects in colliding solids”, Journal Of Computational Physics, 5, (1970).
[2] Fortov V., Kim V., Lomonosov I., Matveichev A., “Numerical modeling of hypervelocity impacts”, International Journal Of Impact Engineering, 33, (2006).
[3] Ghomi M., Mahmoudi J., Khalkhali A., Liaghat G., “Explosive welding of unequal surface using Groove Method”, Transactions Of The Canadian Society For Mechanical Engineering, 36, (2022).
[4] Nassiri A., Kinse B., “Numerical studies on high-velocity impact welding: smoothed particle hydrodynamics (SPH) and arbitrary Lagrangian-Eulerian (ALE)”, Journal Of Manufactur-ing Processes, 24, (2016).
[5] Zhang Z.L., Feng D.L., Liu M.B., “Investigation of explosive welding through whole process modeling using a density adaptive SPH method”, Journal of Manufacturing Processes, 35, (2018).
[6] Rozen A.E., Los' I.S., Muizemnek A.YU., Khorin A.V., “Modelirovanie deformatsionnogo protsessa v zadachakh armirovaniya i svarki vzryvom s primeneniem programmy LS-DYNA”, Izvestiya vuzov. Povolzhskii region. Tekhnicheskie nauki, 13, (2010).
[7] Marinin M.A., Khokhlov S.V., Isheiskii V.A., “Modelirovanie rezhima protekaniya protsessa svarki ploskikh listovykh detalei vzryvom”, Zapiski gornogo instituta, 237, (2019).
[8] Chuprov P., Utkin P., Fortova S., “Numerical Simulation of a High-Speed Impact of Metal Plates Using a Three-Fluid Model”, Metals, 11, (2021).
[9] Fortova S., Utkin P., Kazakova T., “Three-Dimensional Numerical Simulation of the Development of Instability of a Contact Boundary of Colliding Metal Plates within the Gas Dynamic Approximation”, High Temperature, 57, (2019).
[10] Chuprov P.A., Poroshina YA.E., Utkin P.S., “Chislennoe issledovanie deflagratsii porokha v ramkakh modeli Baera-Nuntsiato”, Gorenie i Vzryv, 13, (2020).
[11] Yakovlev I., “Instability of the interface between colliding metals”, Combustion, Explosion And Shock Waves, 9, (1973).
[12] Baer M., Nunziato J., “A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials.”, International Journal Of Multiphase Flow, 12, (1986).
[13] Liang S., Liu W., Yuan L., “Solving seven-equation model for compressible two-phase flow using multiple GPUs”, Computers & Fluids, 99, (2014).
[14] Saurel R., Abgrall R., “A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows”, Journal Of Computational Physics, 150, (1999).
[15] Saurel R., Lemetayer O., “A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation”, Journal Of Fluid Mechanics, 431, (2001).
[16] Inogamov N.A., Dem'yanov A.YU., Son E.E., Gidrodinamika peremeshivaniya, Moskva, 1999.
[17] Layzer D., “On the Instability of Superposed Fluids in a Gravitational Field”, The Astro-physical Journal, 122, (1955).
[18] Goncharov V. N., “Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers”, Physical Review Letters, 88, (2002).
[19] Guillard H., Murrone A., “On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes”, Computers & Fluids, 33, (2004).

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