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

DOI10.1016/j.jcp.2014.06.051zbMath1349.76579OpenAlexW2015400312MaRDI QIDQ349441

Mahmoud A. E. Abdelrahman, Matthias Kunik

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2014.06.051

zbMATH Keywords

conservation lawshyperbolic systemsshock wavesentropy conditionsLorentz transformationsfront tracking schemerarefaction wavesrelativistic Euler equationsnon-entropy shocks

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) (83C55) Quantum hydrodynamics and relativistic hydrodynamics (76Y05)

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Cites Work

• Unnamed Item
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• An improved front tracking method for the Euler equations
• Local existence of weak solutions to the quasi-linear wave equation for large initial values
• A front tracking method for conservation laws in one dimension
• Global solutions of systems of conservation laws by wave-front tracking
• Global existence of solutions to nonlinear hyperbolic systems of conservation laws
• Global solutions of the relativistic Euler equations
• On the front-tracking algorithm
• The interaction of waves for the ultra-relativistic Euler equations
• Second order front tracking for the Euler equations
• Polygonal approximations of solutions of the initial value problem for a conservation law
• Front Tracking Applied to a Nonstrictly Hyperbolic System of Conservation Laws
• A Front-Tracking Alternative to the Random Choice Method
• Continuous dependence in the large for some equations of gas dynamics
• Discontinuous solutions of non-linear differential equations