M. E. Ladonkina^{1, 2}, Yu. A. Poveschenko^{1, 2}, H. Zhang^{1, 2}

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

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

Abstract. In iterative algorithms for fully conservative difference schemes (FCDS) for the equations of gas dynamics in Euler variables, new methods for selecting adaptive artificial viscosity (AAV) have been developed, which are used both in explicit iterative processes and in the separate tridiagonal matrix algorithm. Various methods for incorporating AAV are discussed in this paper, including those for effectively suppressing oscillations in velocity profiles. All iterative methods are described in detail and block diagrams are given. A grid embedding method for modeling on spatially irregular sects is proposed. Calculations of the classical arbitrary discontinuity decay problem (the Sod problem) using FCDS and the developed AAV methods in different iterative processes have been performed. Comparative analysis is carried out and the efficiency of the developed improved iterative processes and approaches to the choice of AAV in comparison with the works of other authors is shown. All calculations are illustrated. The figures show variants of solutions of the Sod problem on uniform and non-uniform meshes, as well as a comparison of the methods proposed in the paper for the calculation of the Sod problem on a uniform grid.

Key Words: completely conservative difference scheme, method of reference operators, gas dynamics, Sod problem

For citation: M. E. Ladonkina, Yu. A. Poveschenko, H. Zhang. Comparative analysis of some iterative processes for realization of fully conservative difference schemes for gas dynamics equations in Euler variables. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 26:4(2024), 404–423. DOI: https://doi.org/10.15507/2079-6900.26.202404.404-423

Information about the authors:

Marina E. Ladonkina, Ph.D. (Phys. and Math.), Senior researcher, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (4 Miusskaya sq., Moscow, 125047, Russia), ORCID: https://orcid.org/0000-0001-7596-1672, ladonkina@imamod.ru

Yurii A. Poveschenko, D. Sci. (Phys. and Math.), Leading researcher, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (4 Miusskaya sq., Moscow, 125047, Russia) ORCID: https://orcid.org/0000-0001-9211-9057, hecon@mail.ru

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