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 SB RAS, Novosibirsk, Russia
Keywords: математическое моделирование, кусочно-параболический метод на локальном шаблоне, релятивистская гидродинамика, numerical modeling, numerical methods of high accuracy order, special relativistic hydrodynamics
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.
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