Finite volume approximation of the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime
| Autor: | Baver Okutmustur, Tuba Ceylan |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Finite volume method
Spacetime De Sitter space General Mathematics Godunov's scheme 010103 numerical & computational mathematics 01 natural sciences Burgers' equation 010101 applied mathematics General Relativity and Quantum Cosmology Relativistic Burgers equation spacetime Schwarzschild-de Sitter metric Schwarzschild-de Sitter background finite volume method Godunov scheme Anti-de Sitter space 0101 mathematics Schwarzschild radius de Sitter invariant special relativity Mathematical physics Mathematics |
| Zdroj: | Volume: 41, Issue: 4 1027-1041 Turkish Journal of Mathematics |
| ISSN: | 1300-0098 1303-6149 |
| Popis: | 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 second-order 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. |
| Databáze: | OpenAIRE |
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