Open Access

ARTICLE

Methods of Selecting Adaptive Artificial Viscosity in Completely Conservative Difference Schemes for Gas Dynamics Equations in Euler Variables

Marina Ladonkina¹, Viktoriia Podryga^1,*, Yury Poveshchenko¹, Haochen Zhang²
1 Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, 125047, Russia
2 Department of Mathematical Modeling and Applied Mathematics, Phystech School of Applied Mathematics and Computer Science, Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, 141701, Russia
* Corresponding Author: Viktoriia Podryga. Email:
(This article belongs to the Special Issue: Heat and Mass Transfer in Energy Equipment)

Frontiers in Heat and Mass Transfer https://doi.org/10.32604/fhmt.2025.066953

Received 21 April 2025; Accepted 30 July 2025; Published online 11 September 2025

Abstract

The work presents new methods for selecting adaptive artificial viscosity (AAV) in iterative algorithms of completely conservative difference schemes (CCDS) used to solve gas dynamics equations in Euler variables. These methods allow to effectively suppress oscillations, including in velocity profiles, as well as computational instabilities in modeling gas-dynamic processes described by hyperbolic equations. The methods can be applied both in explicit and implicit (method of separate sweeps) iterative processes in numerical modeling of gas dynamics in the presence of heat and mass transfer, as well as in solving problems of magnetohydrodynamics and computational astrophysics. In order to avoid loss of solution accuracy on spatially non-uniform grids, in this work an algorithm of grid embeddings is developed, which is applied near transition points between cells of different sizes. The developed algorithms of CCDS using the methods for AAV selection and the algorithm of grid embeddings are implemented for various iterative processes. Calculations are performed for the classical problem of decay of an arbitrary discontinuity (Sod’s problem) and the problem of propagation of two symmetric rarefaction waves in opposite directions (Einfeldt’s problem). In the case of using different methods for selecting the AAV, a comparison of the solutions of the Sod’s problem on uniform and non-uniform grids and a comparison of the solutions of the Einfeldt’s problem on a uniform grid are performed. As a result of the comparative analysis, the applicability of these methods is shown in the spatially one-dimensional case (explicit and implicit iterative processes). The obtained results are compared with the data from the literature. The results coincide with analytical solutions with high accuracy, where the relative error does not exceed 0.1%, which demonstrates the effectiveness of the developed algorithms and methods.

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Keywords

Gas dynamics; adaptive artificial viscosity; equations in Euler variables; completely conservative difference schemes; heat and mass transfer

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