Second-order accurate kinetic schemes for the ultra-relativistic Euler equations

2003 ◽  
Vol 192 (2) ◽  
pp. 695-726 ◽  
Author(s):  
Matthias Kunik ◽  
Shamsul Qamar ◽  
Gerald Warnecke
Keyword(s):  
Euler Equations ◽  
Second Order ◽  
Relativistic Euler Equations ◽  
Kinetic Schemes

Kinetic schemes for the ultra-relativistic Euler equations

2003 ◽  
Vol 187 (2) ◽  
pp. 572-596 ◽  
Author(s):  
Matthias Kunik ◽  
Shamsul Qamar ◽  
Gerald Warnecke
Keyword(s):  
Euler Equations ◽  
Relativistic Euler Equations ◽  
Kinetic Schemes

scholarly journals Causal dissipation for the relativistic dynamics of ideal gases

2017 ◽  
Vol 473 (2201) ◽  
pp. 20160729 ◽  
Author(s):  
Heinrich Freistühler ◽  
Blake Temple
Keyword(s):  
Euler Equations ◽  
Stokes Equations ◽  
Second Order ◽  
Order System ◽  
Navier Stokes ◽  
Unique Element ◽  
Relativistic Euler Equations ◽  
Navier Stokes Equations ◽  
First Order ◽  
Ideal Gases

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations.

scholarly journals A new variation for the relativistic Euler equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mahmoud A. E. Abdelrahman ◽  
Hanan A. Alkhidhr
Keyword(s):  
Euler Equations ◽  
Nonlinear Waves ◽  
Approximation Scheme ◽  
Strength Function ◽  
Convergent Sequence ◽  
Approximate Solutions ◽  
Large Initial Data ◽  
Initial Value ◽  
Relativistic Euler Equations ◽  
Glimm Scheme

Abstract The Glimm scheme is one of the so famous techniques for getting solutions of the general initial value problem by building a convergent sequence of approximate solutions. The approximation scheme is based on the solution of the Riemann problem. In this paper, we use a new strength function in order to present a new kind of total variation of a solution. Based on this new variation, we use the Glimm scheme to prove the global existence of weak solutions for the nonlinear ultra-relativistic Euler equations for a class of large initial data that involve the interaction of nonlinear waves.

Implicit kinetic schemes for the Euler equations

2003 ◽  
Vol 43 (9) ◽  
pp. 1081-1098
Author(s):  
H. S. R. Reksoprodjo ◽  
R. K. Agarwal
Keyword(s):  
Euler Equations ◽  
Kinetic Schemes
Sign in / Sign up

Export Citation Format

Share Document