A Low-Dissipation Numerical Scheme Based on a Piecewise Parabolic Method on a Local Stencil for Mathematical Modeling of Relativistic Hydrodynamic Flows

ABSTRACT

A low-dissipation numerical method based on a combination of Godunov’s method and a piecewise parabolic method on a local stencil is presented. The construction of the method is described in detail. The method is tested using a one-dimensional problem of breakdown of a discontinuity. The results of a numerical simulation of collision of two relativistic gas spheres are given.

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Funding

This work was supported by the Russian Science Foundation (project no. 18-11-00044).

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Correspondence to I. M. Kulikov.

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Kulikov, I.M. A Low-Dissipation Numerical Scheme Based on a Piecewise Parabolic Method on a Local Stencil for Mathematical Modeling of Relativistic Hydrodynamic Flows. Numer. Analys. Appl. 13, 117–126 (2020). https://doi.org/10.1134/S1995423920020032

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Keywords

  • numerical modeling
  • piecewise parabolic method
  • local stencil
  • relativistic hydrodynamics