This article is cited in 5 papers

The use of the piecewise parabolic method on a local stencil for constructing a low dissipation of a numerical solution scheme for mathematical modeling of special relativistic hydrodynamic flows

I. M. Kulikov

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090 Russia

Abstract: In this paper a new numerical method with a low-dissipation of a numerical solution, based on a combination of the Godunov method with the Roe scheme, and a piecewise parabolic method on a local stencil is described. The construction of the numerical method is described in considerable detail, the method is validated on the one-dimensional Riemann problem. The results of the numerical simulation of the collision of two relativistic gas spheres are presented.

Key words: numerical modeling, numerical methods of high accuracy order, special relativistic hydrodynamics.

UDC: 519.6

Received: 02.05.2018
Revised: 28.03.2019
Accepted: 19.12.2019

DOI: 10.15372/SJNM20200200203

 English version: Numerical Analysis and Applications, 2020, 13:2, 117–126

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