Exact and Numerical Solutions of the Riemann Problem for a Conservative Model of Compressible Two-Phase Flows | Sciact - Система учета научной деятельности ИМ СО РАН

Exact and Numerical Solutions of the Riemann Problem for a Conservative Model of Compressible Two-Phase Flows Научная публикация

Журнал

Journal of Scientific Computing
ISSN: 0885-7474 , E-ISSN: 1573-7691

Вых. Данные

Год: 2022, Том: 93, Номер: 3, Номер статьи : 83, Страниц : DOI: 10.1007/s10915-022-02028-x

Ключевые слова

Comparison with the Baer-Nunziato model; Conservative model of compressible two fluid flow; Exact solution of the Riemann problem; Finite volume schemes; Resonance for non-strictly hyperbolic systems; Thermodynamically compatible hyperbolic systems

Авторы

Thein F. ^1,2 , Romenski E. ^3,4 , Dumbser M. ⁴

Организации

1	Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, PSF 4120, Magdeburg, 39016, Germany
2	Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056, Aachen, Germany
3	Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
4	Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano, 77, Trento, 38123, Italy

Информация о финансировании (1)

Министерство науки и высшего образования РФ
Математический центр в Академгородке

075-15-2019-1613, 075-15-2022-281

In this work we study the solution of the Riemann problem for the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) two-phase flow model introduced in Romenski et al. (J Sci Comput 42(1):68, 2009, Quart Appl Math 65(2):259–279, 2007). All characteristic fields are carefully studied and explicit expressions are derived for the Riemann invariants and the Rankine–Hugoniot conditions. Due to the presence of multiple characteristics in the system under consideration, non-standard wave phenomena can occur. Therefore we briefly review admissibility conditions for discontinuities and then discuss possible wave interactions. In particular we will show that overlapping rarefaction waves are possible and moreover we may have shocks that lie inside a rarefaction wave. In contrast to nonconservative two phase flow models, such as the Baer–Nunziato system, we can use the advantage of the conservative form of the model under consideration. Furthermore, we show the relation between the considered conservative SHTC system and the corresponding barotropic version of the nonconservative Baer–Nunziato model. Additionally, we derive the reduced four equation Kapila system for the case of instantaneous relaxation, which is the common limit system of both, the conservative SHTC model and the non-conservative Baer–Nunziato model. Finally, we compare exact solutions of the Riemann problem with numerical results obtained for the conservative two-phase flow model under consideration, for the non-conservative Baer–Nunziato system and for the Kapila limit. The examples underline the previous analysis of the different wave phenomena, as well as differences and similarities of the three systems. © 2022, The Author(s).

Thein F. , Romenski E. , Dumbser M.
Exact and Numerical Solutions of the Riemann Problem for a Conservative Model of Compressible Two-Phase Flows
Journal of Scientific Computing. 2022. V.93. N3. 83 . DOI: 10.1007/s10915-022-02028-x WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000885082500002
Scopus:	2-s2.0-85137160139
РИНЦ:	52053799
OpenAlex:	W4308933778

БД	Цитирований
Scopus	20
Web of science	15
OpenAlex	21
РИНЦ	12