A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime
| Autor: | Philippe G. LeFloch, Tuba Ceylan, Baver Okutmustur |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
Finite volume method Physics and Astronomy (miscellaneous) Spacetime 010103 numerical & computational mathematics 01 natural sciences Burgers' equation 010101 applied mathematics General Relativity and Quantum Cosmology symbols.namesake Friedmann–Lemaître–Robertson–Walker metric symbols 0101 mathematics Mathematical physics |
| Zdroj: | Communications in Computational Physics. 23 |
| ISSN: | 1815-2406 |
| DOI: | 10.4208/cicp.020415.260717a |
| Popis: | A relativistic generalization of the inviscid Burgers equation was introduced by LeFloch and co-authors and was recently investigated numerically on a Schwarzschild background. We extend this analysis to a Friedmann-Lemaitre-Robertson-Walker (FLRW) background, which is more challenging due to the existence of time-dependent, spatially homogeneous solutions. We present a derivation of the model of interest and we study its basic properties, including the class of spatially homogeneous solutions. Then, we design a second-order accurate scheme based on the finite volume methodology, which provides us with a tool for investigating the properties of solutions. Computational experiments demonstrate the efficiency of the proposed scheme for numerically capturing weak solutions. |
| Databáze: | OpenAIRE |
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