REGULARIZED EQUATIONS FOR DYNAMICS OF THE HETEROGENEOUS BINARY MIXTURES OF THE NOBLE-ABEL STIFFENED-GASES AND THEIR APPLICATION
- Авторлар: Zlotnik A.1,2, Lomonosov T.1,2
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Мекемелер:
- Higher School of Economics University
- Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
- Шығарылым: Том 514, № 1 (2023)
- Беттер: 26-33
- Бөлім: МАТЕМАТИКА
- URL: https://journals.rcsi.science/2686-9543/article/view/247080
- DOI: https://doi.org/10.31857/S2686954323600313
- EDN: https://elibrary.ru/DEJANK
- ID: 247080
Дәйексөз келтіру
Аннотация
We consider the so-called four-equation model for dynamics of the heterogeneous compressible binary mixtures with the Noble-Abel stiffened-gas equations of state. We exploit its quasi-homogeneous form arising after excluding the volume concentrations from the sought functions and based on a quadratic equation for the common pressure of the components. We present new properties of this equation and a simple formula for the squared speed of sound, suggest an alternative derivation for a formula relating it to the squared Wood speed of sound and state the pressure balance equation. For the first time, we give quasi-gasdynamic-type regularization of the heterogeneous model (in the quasi-homogeneous form), construct explicit two-level in time and symmetric three point in space finite-difference scheme without limiters to implement it in the 1D case and present numerical results.
Авторлар туралы
A. Zlotnik
Higher School of Economics University; Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
Хат алмасуға жауапты Автор.
Email: azlotnik@hse.ru
Russia, Moscow; Russia, Moscow
T. Lomonosov
Higher School of Economics University; Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
Хат алмасуға жауапты Автор.
Email: tlomonosov@hse.ru
Russia, Moscow; Russia, Moscow
Әдебиет тізімі
- Flätten T., Morin A., Munkejord S.T. // SIAM J. Appl. Math. 2010. V. 70. P. 2861–2882.
- Zhang C., Menshov I., Wang L., Shen Z. // J. Comput. Phys. 2022. V. 466, article 111356.
- Le Métayer O., Saurel R. // Phys. Fluids. 2016. V. 28. P. 046102.
- Le Martelot S., Saurel R., Nkonga B. // Int. J. Multiphase Flow. 2014. V. 66. P. 62–78.
- Saurel R., Boivin P., Le Métayer O. // Comput. Fluids. 2016. V. 128. P. 53–64.
- Chiapolino A., Boivin P., Saurel R. // Int. J. Numer. Meth. Fluids. 2017. V. 83. P. 583–605.
- Pelanti M. // Int. J. Multiphase Flow. 2022. V. 153, article 104097.
- Четверушкин Б.Н. Кинетические схемы и квазигазодинамическая система уравнений. М.: МАКС Пресс, 2004.
- Елизарова Т.Г. Квазигазодинамические уравнения и методы расчета вязких течений. М.: Научный мир, 2007.
- Zlotnik A., Lomonosov T. // Entropy. 2023. V. 25, article 158.
- Злотник А.А. // Матем. моделирование. 2012. Т. 24. № 4. С. 65–79.
- Злотник А.А. // ЖВМиМФ. 2012. Т. 52. № 7. С. 1304–1316.
- Злотник А.А., Ломоносов Т.А. // ДАН. 2018. Т. 482. № 4. С. 375–380.
- Li Q., Fu S. // Comput. Math. Appl. 2011. V. 61. P. 3639–3652.
- Zlotnik A., Lomonosov T. // Chaos. 2023. V. 33, article 113128.