scholarly journals Excision methods for high resolution shock capturing schemes applied to general relativistic hydrodynamics

2005 ◽  
Vol 71 (10) ◽  
Author(s):  
Ian Hawke ◽  
Frank Löffler ◽  
Andrea Nerozzi
Keyword(s):  
High Resolution ◽  
Shock Capturing ◽  
Relativistic Hydrodynamics ◽  
Shock Capturing Schemes ◽  
General Relativistic

The analytical solution of the Riemann problem in relativistic hydrodynamics

1994 ◽  
Vol 258 ◽  
pp. 317-333 ◽  
Author(s):  
José Ma Martí ◽  
Ewald Müller
Keyword(s):  
High Resolution ◽  
Analytical Solution ◽  
Riemann Problem ◽  
Shock Capturing ◽  
Relativistic Hydrodynamics ◽  
Minkowski Space Time ◽  
Intermediate States ◽  
Relativistic Flow ◽  
Initial Discontinuity ◽  
The Impact

We consider the decay of an initial discontinuity in a polytropic gas in a Minkowski space–time (the special relativistic Riemann problem). In order to get a general analytical solution for this problem, we analyse the properties of the relativistic flow across shock waves and rarefactions. As in classical hydrodynamics, the solution of the Riemann problem is found by solving an implicit algebraic equation which gives the pressure in the intermediate states. The solution presented here contains as a particular case the special relativistic shock-tube problem in which the gas is initially at rest. Finally, we discuss the impact of this result on the development of high-resolution shock-capturing numerical codes to solve the equations of relativistic hydrodynamics.

A HIGH ORDER KINETIC FLUX-SPLITTING METHOD FOR THE SPECIAL RELATIVISTIC HYDRODYNAMICS

2005 ◽  
Vol 02 (01) ◽  
pp. 49-74 ◽  
Author(s):  
SHAMSUL QAMAR ◽  
GERALD WARNECKE
Keyword(s):  
High Resolution ◽  
Kinetic Theory ◽  
Splitting Method ◽  
High Order ◽  
Shock Capturing ◽  
High Order Accuracy ◽  
Order Kinetic ◽  
Relativistic Hydrodynamics ◽  
Order Accuracy ◽  
Flux Splitting

In this article we present a flux splitting method based on gas-kinetic theory for the special relativistic hydrodynamics (SRHD) [Landau and Lifshitz, Fluid Mechanics, Pergamon New York, 1987] in one and two space dimensions. This kinetic method is based on the direct splitting of the macroscopic flux functions with the consideration of particle transport. At the same time, particle "collisions" are implemented in the free transport process to reduce numerical dissipation. Due to the nonlinear relations between conservative and primitive variables and the consequent complexity of the Jacobian matrix, the multi-dimensional shock-capturing numerical schemes for SRHD are computationally more expensive. All the previous methods presented for the solution of these equations were based on the macroscopic continuum description. These upwind high-resolution shock-capturing (HRSC) schemes, which were originally made for non-relativistic flows, were extended to SRHD. However our method, which is based on kinetic theory is more related to the physics of these equations and is very efficient, robust, and easy to implement. In order to get high order accuracy in space, we use a third order central weighted essentially non-oscillatory (CWENO) finite difference interpolation routine. To achieve high order accuracy in time we use a Runge-Kutta time stepping method. The one- and two-dimensional computations reported in this paper show the desired accuracy, high resolution, and robustness of the method.

scholarly journals Comparative study of high-resolution shock-capturing schemes for a real gas

AIAA Journal ◽  
1989 ◽  
Vol 27 (10) ◽  
pp. 1332-1346 ◽  
Author(s):  
J.-L. Montagne ◽  
H. C. Yee ◽  
M. Vinokur
Keyword(s):  
High Resolution ◽  
Comparative Study ◽  
Shock Capturing ◽  
Real Gas ◽  
Shock Capturing Schemes
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