A new front tracking scheme for the ultra-relativistic Euler equations

The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure p, the spatial part u∈R3 of the dimensionless four-velocity and the particle density n. Two schemes for these equations are presented in one space dimension, namely a front tracking and a cone-grid scheme....

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational physics 2014-10, Vol.275, p.213-235
Main Authors: Abdelrahman, Mahmoud A.E., Kunik, Matthias
Format: Article
Language:English
Subjects:
Approximation
Conservation laws
Constants
Density
Discontinuity
Entropy conditions
Euler equations
Front tracking scheme
Hyperbolic systems
Lorentz transformations
Mathematical analysis
Mathematical models
Non-entropy shocks
Rarefaction waves
Relativistic Euler equations
Shock waves
Tracking
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure p, the spatial part u∈R3 of the dimensionless four-velocity and the particle density n. Two schemes for these equations are presented in one space dimension, namely a front tracking and a cone-grid scheme. A new front tracking technique for the ultra-relativistic Euler equations is introduced, which gives weak solutions. The front tracking method is based on piecewise constant approximations to Riemann solutions, called front tracking Riemann solutions, where continuous rarefaction waves are approximated by finite collections of discontinuities, so-called non-entropy shocks. This method can be used for analytical as well as for numerical purposes. A new unconditionally stable cone-grid scheme is also derived in this paper, which is based on the Riemann solution for the ultra-relativistic Euler equations. Both schemes are compared by two numerical examples, where explicit solutions are known.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.06.051