Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study

Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study

Year:    2021

Author:    Yangyang Cao, Mohammad A. Ghazizadeh, Philippe G. LeFloch

Communications in Computational Physics, Vol. 29 (2021), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2020-0033

Communications in Computational Physics, Vol. 29 (2021), Iss. 2 : pp. 472–509

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    38

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

Author Details

Yangyang Cao

Mohammad A. Ghazizadeh

Philippe G. LeFloch

  1. Asymptotic structure of cosmological fluid flows: a numerical study

    Cao, Yangyang

    Ghazizadeh, Mohammad A.

    LeFloch, Philippe G.

    Communications in Applied Mathematics and Computational Science, Vol. 17 (2022), Iss. 1 P.79

    https://doi.org/10.2140/camcos.2022.17.79 [Citations: 1]