Quasi-Gasdynamic Model and Numerical Algorithm for Describing Mixtures of Different Fluids

T. G. Elizarova; Елизарова Т. Г.; E. V. Shil’nikov; Шильников Е. В.

doi:10.31857/S0044466923070050

Quasi-Gasdynamic Model and Numerical Algorithm for Describing Mixtures of Different Fluids

Authors: Elizarova T.G.¹, Shil’nikov E.V.¹
Affiliations:
1. Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
Issue: Vol 63, No 7 (2023)
Pages: 1193-1205
Section: МАТЕМАТИЧЕСКАЯ ФИЗИКА
URL: https://journals.rcsi.science/0044-4669/article/view/136194
DOI: https://doi.org/10.31857/S0044466923070050
EDN: https://elibrary.ru/ZXOZPY
ID: 136194

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Abstract
About the authors
References
Supplementary files
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Abstract

An elegant and easy-to-implement numerical algorithm for simulating flows of homogeneous gas mixtures with component temperatures and velocities assumed to be equal is constructed and tested. The algorithm yields monotone density profiles for the components even if their specific heat ratios are widely different. The algorithm can be used to simulate some flows of gas–liquid mixtures.

Keywords

homogeneous gas mixture, one-fluid approximation, finite-difference algorithm, regularized equations

About the authors

T. G. Elizarova

Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Email: telizar@mail.ru
125047, Moscow, Russia

E. V. Shil’nikov

Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Author for correspondence.
Email: shilnikov@imamod.ru
125047, Moscow, Russia

References

Лифшиц Е.М., Питаевский Л.П. Физическая кинетика. М.: Физматлит, 2002.
Зельдович Я.Б., Райзер Ю.П. Физика ударных волн и высокотемпературных гидродинамических явлений. М.: Наука, 1966.
Головачев Ю.П. Численное моделирование течений газа в ударном слое. М.: Наука, Физматлит, 1996.
Елизарова Т.Г. Квазигазодинамические уравнения и методы расчета газодинамических течений. М.: Научный мир, 2007.
Elizarova T.G., Zlotnik A.A., Shil’nikov E.V. Regularized equations for numerical simulation of flows of homogeneous binary mixtures of viscous compressible gases // Comp. Math. and Math. Phys. 2019. V. 59. № 11. P. 1832–1847.https://doi.org/10.1134/S0965542519110058
Elizarova T.G., Shil’nikov E.V. Numerical simulation of gas mixtures based on the quasi-gasdynamic approach as applied to the interaction of shock wave with a gas bubble // Comp. Math. and Math. Phys. 2021. V. 61. № 1. P. 118–128.https://doi.org/10.1134/S096554252101004
Shilnikov E.V., Elizarova T.G. About one numerical method of compressible multifluid flow modelling in Euler formulation. In: Proc. IRF2020: 7th Inter. Conf. Integrity–Reliability–Failure. J.F. Silva Gomes and S.A. Meguid (ed.), INEGI-FEUP, 2020. P. 613–622.
Хайталиев И.Р., Шильников Е.В. Исследование свойств квазигазодинамической системы уравнений на решении задачи Римана для смеси газов. Препринт ИПМ им. М.В. Келдыша РАН, № 52 2021 г. (перевод: Shilnikov E.V., Khaytaliev I.R. Investigation of the properties of a quasi-gas-dynamic system of equations based on the solution of the Riemann problem for a mixture of gases. Preprints KIAM RAS, 2021, № 52, 12 p).
Abgrall R., Karni S. Computations of compressible multifluids // J. Comp. Phys. 2001. № 2. P. 594–623.
Banks J.W., Schwendeman D.W., Karila A.K., Henshaw W.D. A high-resolution Godunov method for compressible multi-material flow on overlapping grids // J. Comp. Phys. 2007. V. 223. Iss. 1. P. 262–297.
Borisov V.E. and Rykov Yu.G. Modified Godunov method for multicomponent flow simulation // J. Phys.: Conf. Ser. 2019. 1250 012006. https://doi.org/10.1088/1742-6596/1250/1/012006
Борисов В.Е., Рыков Ю.Г. Численное моделирование течений многокомпонентных газовых смесей с использованием метода двойного потока // Матем. моделирование. 2020. Т. 32. № 9. С. 15–29.
Zlotnik A., Fedchenko A., Lomonosov T. Entropy correct spatial discretizations for 1D regularized systems of equations for gas mixture dynamics // Symmetry. 2022. V. 14. P. 2171.https://doi.org/10.3390/sym14102171
github.com/unicfdlab/QGDsolver
Kraposhin M.V., Smirnova E.V., Elizarova T.G., Istomina M.A. Development of a new OpenFOAM solver using regularized gas dynamic equations // Comp. & Fluid. 2018. V. 166. P. 163–175.https://doi.org/10.1016/j.compfluid.2018.02.010
Елизарова Т.Г. Осреднение по времени как приближенный способ построения квазигазодинамических и квазигидродинамических уравнений // Ж. вычисл. матем. и матем. физ. 2011. Т. 51. № 11. С. 2096–2105 (перевод: Elizarova T.G. Time averaging as an approximate technique for constructing quasi-gasdynamic and quasi-hydrodynamic equations // Comp. Math. and Math. Phys. 2011. V. 51. № 11. P. 1973–1982).
Шеретов Ю.В. Динамика сплошных сред при пространственно-временном осреднении. М.-Ижевск, 2009.
Denner F., Cheng-Nian Xiao, Berend G.M. van Wachem Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretization // J. Comp. Phys. 2018. V. 367. P. 192–234. ISSN 0021-9991.https://doi.org/10.1016/j.jcp.2018.04.028
Keiichi Kitamura, Meng-Sing Liou1, Chih-Hao Chang Extension and comparative study of AUSM-family schemes for compressible multiphase flow simulations // Commun. Comp. Phys. 2014. V. 16. № 3. C. 632–674. https://doi.org/10.4208/cicp.020813.190214a
Liou, Meng-Sing, Chih Chang, Loc Hoang Nguyen, Theo G. Theofanous How to solve compressible multifluid equations: a simple, robust and accurate method // AIAA J. 2007. V. 46. P. 2345–2356.