DOI 10.15507/2079-6900.23.202104.412–423

Original article

ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

MSC2020 65M22

Theoretical Analysis of Fully Conservative Difference Schemes with Adaptive Viscosity

M. E. Ladonkina1, 2, Yu. A. Poveshenko1, 2, O. R. Ragimli1, H. Zhang1, 2

1Keldysh Institute of Applied Mathematics (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 two-layer in time completely conservative difference schemes with space-profiled time weights is constructed. Considerable attention is paid to the methods of constructing regularized flows of mass, momentum, and internal energy that do not violate the properties of complete conservatism of difference schemes of this class, to the analysis of their amplitudes and the possibility of their use on non-uniform grids. Effective preservation of the balance of internal energy in this type of divergent difference schemes is ensured by the absence of constantly operating sources of difference origin that produce "computational"entropy (including those based on singular features of the solution). The developed schemes can be easily generalized in order to calculate high-temperature flows in media that are nonequilibrium in temperature (for example, in a plasma with a difference in the temperatures of the electronic and ionic components), when, with the set of variables necessary for describing the flow, it is not enough to equalize the total energy balance.

Key Words: completely conservative difference schemes, support operator method, gas dynamics

For citation: M. E. Ladonkina, Yu. A. Poveshenko, O. R. Ragimli, H. Zhang. Theoretical Analysis of Fully Conservative Difference Schemes with Adaptive Viscosity . Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 23:4(2021), 412–423. DOI: https://doi.org/10.15507/2079-6900.23.202104.412–423

Submitted: 14.09.2021; Revised: 12.11.2021; Accepted: 16.11.2021

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), Ph. D. (Physics and Mathematics), ORCID: https://orcid.org/0000-0001-7596-1672, ladonkina@imamod.ru

Yuri A. Poveshenko, Leading Researcher, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (4 Miusskaya sq., Moscow 125047, Russia), D. 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 per., Dolgoprudny 141701, Russia), ORCID: https://orcid.org/0000-0001-7257-1660, orxan@reximli.info

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

All authors have read and approved the final manuscript.

Conflict of interest: The authors declare no conflict of interest.

Creative Commons Attribution 4.0 International License This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License.