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Volume 23, Issue 2
A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime

Tuba Ceylan, Philippe G. LeFloch & Baver Okutmustur

DOI: 10.4208/cicp.020415.260717a

Commun. Comput. Phys., 23 (2018), pp. 500-519.

Published online: 2018-02

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  • Abstract

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-Lemaître-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.

  • Keywords

Relativistic Burgers equation, FLRW metric, hyperbolic balance law, finite volume scheme.

  • AMS Subject Headings

35L65, 76N10, 83A05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-23-500, author = {Tuba Ceylan, Philippe G. LeFloch and Baver Okutmustur}, title = {A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {2}, pages = {500--519}, abstract = {

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-Lemaître-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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.020415.260717a}, url = {http://global-sci.org/intro/article_detail/cicp/10535.html} }
TY - JOUR T1 - A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime AU - Tuba Ceylan, Philippe G. LeFloch & Baver Okutmustur JO - Communications in Computational Physics VL - 2 SP - 500 EP - 519 PY - 2018 DA - 2018/02 SN - 23 DO - http://doi.org/10.4208/cicp.020415.260717a UR - https://global-sci.org/intro/article_detail/cicp/10535.html KW - Relativistic Burgers equation, FLRW metric, hyperbolic balance law, finite volume scheme. AB -

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-Lemaître-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.

Tuba Ceylan, Philippe G. LeFloch and Baver Okutmustur. (2018). A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime. Communications in Computational Physics. 23 (2). 500-519. doi:10.4208/cicp.020415.260717a
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