Finite volume method for the relativistic burgers model on a (1+1)-Dimensional de sitter spacetime

Ceylan, Tuba
Okutmuştur, Baver
Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our relativistic model by a technique based on the vanishing pressure Euler equations of relativistic compressible fluids on a (1+1)-dimensional background and construct a second order Godunov type finite volume scheme to examine numerical experiments within an analysis of the cosmological constant. Numerical results demonstrate the efficiency of the method for solutions containing shock and rarefaction waves.
Mathematical and Computational Applications


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Ceylan, Tuba; Okutmuştur, Baver (2017-01-01)
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 there lativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime and introduce a second-order Godunov-type finite volume scheme for the approximation of discontinuous solutions to the model of interest. The effect of the cosmological constantis also taken i...
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Citation Formats
T. Ceylan and B. Okutmuştur, “Finite volume method for the relativistic burgers model on a (1+1)-Dimensional de sitter spacetime,” Mathematical and Computational Applications, pp. 0–0, 2016, Accessed: 00, 2020. [Online]. Available: