Finite volume approximation of the relativistic Burgers equation on a Schwarzschild--(anti-)de Sitter spacetime | Zendy

Tuba Ceylan | Zendy; Baver Okutmuştur | Zendy

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Finite volume approximation of the relativistic Burgers equation on a Schwarzschild--(anti-)de Sitter spacetime

Author(s) -

Tuba Ceylan,

Baver Okutmuştur

Publication year - 2017

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1602-38

Subject(s) - schwarzschild radius , friedmann–lemaître–robertson–walker metric , finite volume method , spacetime , mathematical physics , de sitter universe , burgers' equation , classical mechanics , physics , mathematics , mathematical analysis , universe , quantum mechanics , partial differential equation

The relativistic versions of Burgers equations on the Schwarzschild, FLRW, and de Sitter backgrounds have recently been derived and analyzed numerically via finite volume approximation based on the concerned models. In this work, we derive the relativistic Burgers equation on a Schwarzschild–(anti-)de Sitter spacetime and introduce a secondorder Godunov-type finite volume scheme for the approximation of discontinuous solutions to the model of interest. The effect of the cosmological constant is also taken into account both theoretically and numerically. The efficiency of the method for solutions containing shock and rarefaction waves are presented by several numerical experiments.

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