M. E. Ladonkina^{1, 2}, Yu. A. Poveshenko^{1, 2}, O. R. Ragimli², H. Zhang²

¹Keldysh Institute of Applied Mathematics of RAS (Moscow, Russian Federation)

²Moscow Institute of Physics and Technology (Dolgoprudny, Russian Federation)

Abstract. For the equations of gas dynamics in Eulerian variables, a family of twolayer time-fully conservative difference schemes (FCDS) with space-profiled time weights is investigated. Nodal schemes and a class of divergent adaptive viscosities for FCDS with spacetime profiled weights connected with variable masses of moving nodal particles of the medium are developed. Considerable attention is paid to the methods of constructing regularized flows of mass, momentum and internal energy that preserve the properties of fully conservative difference schemes of this class, to the analysis of their stability and to the possibility of their use on uneven grids. The effective preservation of the internal energy balance in this class of divergent difference schemes is ensured by the absence of constantly operating sources of difference origin that produce “computational” entropy (including entropy production on the singular features of the solution). Developed schemes may be used in modelling of hightemperature flows in temperature-disequilibrium media, for example, if it is necessary to take into account the electron-ion relaxation of temperature in a short-living plasma under conditions of intense energy input.

Key Words: gas dynamics, support operator method, fully conservative difference schemes, stability of the scheme

For citation: M. E. Ladonkina, Yu. A. Poveshenko, O. R. Ragimli, H. Zhang. Theoretical study of stability of nodal completely conservative difference schemes with viscous filling for gas dynamics equations in Euler variables. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 24:3(2022), 317–330. DOI: https://doi.org/10.15507/2079-6900.24.202203.317-330

Information about the authors:

Marina E. Ladonkina, Senior Researcher , Keldysh Institute of Applied Mathematics of Russian Academy of Sciences(4 Miusskaya Sq., Moscow 125047, Russia), PhD (Physics and Mathematics), ORCID: 0000-0001-7596-1672, e-mail: ladonkina@imamod.ru

Yuri A. Poveshenko, Leading Researcher, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (4 Miusskaya Sq., Moscow 125047, Russia), Dr.Sci. (Physics and Mathematics), ORCID: https://orcid.org/0000-0001-9211-9057, hecon@mail.ru

Orkhan R. Ragimli, Postgraduate Student, Moscow Institute of Physics and Technology (9 Institutskiy Pereulok St., Dolgoprudny 141701, Russia), ORCID: https://orcid.org/0000-0001-7257-1660, orxan@reximli.info

Haochen Zhang, Postgraduate Student, Moscow Institute of Physics and Technology (9 Institutskiy Pereulok St., Dolgoprudny 141701, Russia), ORCID: https://orcid.org/0000-0003-1378-1777, chzhan.h@phystech.edu