R. V. Zhalnin¹, A. I. Kulyagin², M. S. Nefedov²

¹Lavrentyev Institute of Hydrodynamics SB RAS (Novosibirsk, Russian Federation)

²National Research Mordovia State University (Saransk, Russian Federation)

Abstract. This article examines application of computational algorithms with an increased order of accuracy for modeling two-dimensional problems of development of hydrodynamic instabilities. The efficiency of using algorithms to improve the accuracy and reliability of modeling in this area is considered. More specifically, the paper describes a numerical algorithm for solving the problem of development of Richtmayer-Meshkov instability. To construct the algorithm, the authors use the WENO scheme of the fifth order of accuracy Several problems are solved numerically using the developed method. The article models such processes as flows at a time of 4 046 microseconds, a change in the width of the region filled with sulfur hexafluoride, numerical schlieren patterns at a time of 877 microseconds, a change in the width of the region filled with heavy gas. The results are obtained by various methods on grids of different dimensions and compared with experimental data. It is shown that schemes with WENO reconstruction of the 5th order of accuracy demonstrate results closer to full-scale experiments.

Key Words: WENO, gas dynamics, adaptive grids, Richtmayer-Meshkov instability

For citation: R. V. Zhalnin, A. I. Kulyagin, M. S. Nefedov. Application of computational algorithms with higher order of accuracy to the modeling of two-dimensional problems on development of hydrodynamic instability. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 26:2(2024), 143–156. DOI: https://doi.org/10.15507/2079-6900.26.202402.143-156

Information about the authors:

Ruslan V. Zhalnin, Ph.D. (Phys.-Math.), Researcher at the Lavrentiev Institute of Hydrodynamics SB RAS (15 Akademik Lavryentyev Av., Novosibirsk 630090, Russia), ORCID: https://orcid.org/0000-0002-1103-3321, zhrv@mrsu.ru

Andrey I. Kulyagin, Ph.D. (Phys.-Math.), Lecturer at the Department of Applied Mathematics, Differential equations and theoretical mechanics, National Research Mordovia State University (68 Bolshevistskaya Str., Saransk 430005, Republic of Mordovia, Russia), ORCID: https://orcid.org/0009-0005-3158-6221, andreycoolyagin@gmail.com

Michael S. Nefedov, Ph.D. (Phys.-Math.), Lecturer at the Department of Applied Mathematics, Differential equations and theoretical mechanics, National Research Mordovia State University (68 Bolshevistskaya Str., Saransk 430005, Republic of Mordovia, Russia), ORCID: https://orcid.org/0009-0002-7347-2191, snef7@yandex.ru