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A Piecewise-Linear Reconstruction to Reduce the Dissipation of the HLL Method in Solving the Gas Dynamics Equations

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Abstract

In this paper, the construction of the original “Harten–Lax–van Leer” method using a piecewise-linear reconstruction of physical variables is described. The thus obtained numerical method makes it possible to reproduce the pressure, density, and velocity profiles with low dissipation at the discontinuities. To verify the method, classical problems of discontinuity breakdown are used with analytical solutions based on various configurations of shock waves, contact discontinuities, and rarefaction waves. The order of accuracy of the numerical method is studied using a Sod-type problem. It is shown that the greatest decrease in the order of accuracy is when a rarefaction wave is reproduced. The numerical method is verified by means of a three-dimensional Sedov test of a point explosion and a problem of a supernova Ia type explosion with two symmetric ignition points leading to the formation of a G1.9+0.3-type remnant.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    I. M. Kulikov

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Correspondence to I. M. Kulikov.

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Translated from Sibirskii Zhurnal Vychislitel’noi Matematiki, 2022, Vol. 25, No. 2, pp. 141-156. https://doi.org/10.15372/SJNM20220204.

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Kulikov, I.M. A Piecewise-Linear Reconstruction to Reduce the Dissipation of the HLL Method in Solving the Gas Dynamics Equations. Numer. Analys. Appl. 15, 112–124 (2022). https://doi.org/10.1134/S1995423922020045

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  • DOI: https://doi.org/10.1134/S1995423922020045

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