This article is available for purchase or by subscription. See below.
Abstract
|
We consider an isothermal compressible fluid evolving on a cosmological background
which is either expanding or contracting toward the future. The Euler equations
governing such a flow consist of two nonlinear hyperbolic balance laws which we treat
in one and in two space dimensions. We design a finite volume scheme which is
fourth-order accurate in time and second-order accurate in space. This scheme allows
us to compute weak solutions containing shock waves and, by design, is well-balanced
in the sense that it preserves exactly a special class of solutions. Using this scheme,
we investigate the asymptotic structure of the fluid when the time variable
approaches infinity (in the expanding regime) or approaches zero (in the
contracting regime). We study these two limits by introducing a suitable rescaling
of the density and velocity variables and, in turn, we analyze the effects
induced by the geometric terms (of expanding or contracting nature) and the
nonlinear interactions between shocks. Extensive numerical experiments
in one and two space dimensions are performed in order to support our
observations.
|
PDF Access Denied
We have not been able to recognize your IP address
18.217.220.114
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
cosmological Euler model, shock wave, asymptotic structure,
finite volume scheme, geometry-preserving, high-order
accuracy
|
Mathematical Subject Classification 2010
Primary: 76L05, 76M12
Secondary: 83F05
|
Milestones
Received: 16 February 2020
Revised: 24 November 2021
Accepted: 12 December 2021
Published: 7 October 2022
|
|