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 - <p style="text-align: justify;">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.</p>