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.