full
search.png

Search

close.png

Cancel

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

Yangyang Cao, Mohammad A. Ghazizadeh & Philippe G. LeFloch

DOI: 10.4208/cicp.OA-2020-0033

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

Published online: 2020-12

Preview Purchase PDF 2406 37550

Cited by

google scholar semantic scholar
Export citation
  • 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

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-29-472, author = {Cao , YangyangA. 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.

Cao , YangyangA. Ghazizadeh , Mohammad and G. LeFloch , Philippe. (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
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard