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

摘要

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.