Relativistic Hydrodynamics and Essentially Non-oscillatory Shock Capturing Schemes

1995 ◽  
Vol 120 (2) ◽  
pp. 266-277 ◽  
Author(s):  
A. Dolezal ◽  
S.S.M. Wong
Keyword(s):  
Shock Capturing ◽  
Relativistic Hydrodynamics ◽  
Shock Capturing Schemes

scholarly journals Linearly implicit all Mach number shock capturing schemes for the Euler equations

2019 ◽  
Vol 393 ◽  
pp. 278-312 ◽  
Author(s):  
Stavros Avgerinos ◽  
Florian Bernard ◽  
Angelo Iollo ◽  
Giovanni Russo
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Shock Capturing ◽  
Shock Capturing Schemes

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.

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