Volume 29, Issue 2
Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study

Yangyang Cao, Mohammad A. GhazizadehPhilippe G. LeFloch

Commun. Comput. Phys., 29 (2021), pp. 472-509.

Published online: 2020-12

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  • Abstract

We study the cosmological Burgers model, as we call it, which is a nonlinear hyperbolic balance law (in one and two spatial variables) posed on an expanding or contracting background. We design a finite volume scheme that is fourth-order in time and second-order in space, and allows us to compute weak solutions containing shock waves. Our main contribution is the study of the asymptotic structure of the solutions as the time variable approaches infinity (in the expanding case) or zero (in the contracting case). We discover that a saddle competition is taking place which involves, on one hand, the geometrical effects of expanding or contracting nature and, on the other hand, the nonlinear interactions between shock waves.

  • Keywords

Cosmological Burgers model, shock wave, asymptotic structure, finite volume scheme, second-order accuracy, Runge-Kutta scheme.

  • AMS Subject Headings

76L05, 83F05, 76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-472, author = {Cao , Yangyang and A. Ghazizadeh , Mohammad and G. LeFloch , Philippe}, title = {Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {2}, pages = {472--509}, abstract = {

We study the cosmological Burgers model, as we call it, which is a nonlinear hyperbolic balance law (in one and two spatial variables) posed on an expanding or contracting background. We design a finite volume scheme that is fourth-order in time and second-order in space, and allows us to compute weak solutions containing shock waves. Our main contribution is the study of the asymptotic structure of the solutions as the time variable approaches infinity (in the expanding case) or zero (in the contracting case). We discover that a saddle competition is taking place which involves, on one hand, the geometrical effects of expanding or contracting nature and, on the other hand, the nonlinear interactions between shock waves.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0033}, url = {http://global-sci.org/intro/article_detail/cicp/18480.html} }
TY - JOUR T1 - Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study AU - Cao , Yangyang AU - A. Ghazizadeh , Mohammad AU - G. LeFloch , Philippe JO - Communications in Computational Physics VL - 2 SP - 472 EP - 509 PY - 2020 DA - 2020/12 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0033 UR - https://global-sci.org/intro/article_detail/cicp/18480.html KW - Cosmological Burgers model, shock wave, asymptotic structure, finite volume scheme, second-order accuracy, Runge-Kutta scheme. AB -

We study the cosmological Burgers model, as we call it, which is a nonlinear hyperbolic balance law (in one and two spatial variables) posed on an expanding or contracting background. We design a finite volume scheme that is fourth-order in time and second-order in space, and allows us to compute weak solutions containing shock waves. Our main contribution is the study of the asymptotic structure of the solutions as the time variable approaches infinity (in the expanding case) or zero (in the contracting case). We discover that a saddle competition is taking place which involves, on one hand, the geometrical effects of expanding or contracting nature and, on the other hand, the nonlinear interactions between shock waves.

Yangyang Cao, Mohammad A. Ghazizadeh & Philippe G. LeFloch. (2020). Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study. Communications in Computational Physics. 29 (2). 472-509. doi:10.4208/cicp.OA-2020-0033
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