scholarly journals An Exact Riemann Solver for Multidimensional Special Relativistic Hydrodynamics

2001 ◽  
pp. 699-705
Author(s):  
J. A. Pons ◽  
J. M. Marti ◽  
E. Mueller
Keyword(s):  
Riemann Solver ◽  
Relativistic Hydrodynamics ◽  
Exact Riemann Solver

The development of a Riemann solver for the steady supersonic Euler equations

1994 ◽  
Vol 98 (979) ◽  
pp. 325-339 ◽  
Author(s):  
E. F. Toro ◽  
A. Chakraborty
Keyword(s):  
Euler Equations ◽  
Weighted Average ◽  
Godunov Method ◽  
Riemann Solver ◽  
Flux Method ◽  
First Order ◽  
Enhanced Resolution ◽  
Average Flux ◽  
Exact Riemann Solver ◽  
Order Weighted Average

Abstract An improved version (HLLC) of the Harten, Lax, van Leer Riemann solver (HLL) for the steady supersonic Euler equations is presented. Unlike the HLL, the HLLC version admits the presence of the slip line in the structure of the solution. This leads to enhanced resolution of computed slip lines by Godunov type methods. We assess the HLLC solver in the context of the first order Godunov method and the second order weighted average flux method (WAF). It is shown that the improvement embodied in the HLLC solver over the HLL solver is virtually equivalent to incorporating the exact Riemann solver.

scholarly journals An improved exact Riemann solver for relativistic hydrodynamics

2001 ◽  
Vol 449 ◽  
pp. 395-411 ◽  
Author(s):  
LUCIANO REZZOLLA ◽  
OLINDO ZANOTTI
Keyword(s):  
Riemann Problem ◽  
Initial Conditions ◽  
Wave Pattern ◽  
Initial Guess ◽  
Relativistic Velocity ◽  
Riemann Solver ◽  
Rarefaction Waves ◽  
Riemann Solvers ◽  
Velocity Jump ◽  
Exact Riemann Solver

A Riemann problem with prescribed initial conditions will produce one of three possible wave patterns corresponding to the propagation of the different discontinuities that will be produced once the system is allowed to relax. In general, when solving the Riemann problem numerically, the determination of the specific wave pattern produced is obtained through some initial guess which can be successively discarded or improved. We here discuss a new procedure, suitable for implementation in an exact Riemann solver in one dimension, which removes the initial ambiguity in the wave pattern. In particular we focus our attention on the relativistic velocity jump between the two initial states and use this to determine, through some analytic conditions, the wave pattern produced by the decay of the initial discontinuity. The exact Riemann problem is then solved by means of calculating the root of a nonlinear equation. Interestingly, in the case of two rarefaction waves, this root can even be found analytically. Our procedure is straightforward to implement numerically and improves the efficiency of numerical codes based on exact Riemann solvers.

scholarly journals A Numerical Study of Relativistic Jets

1996 ◽  
Vol 175 ◽  
pp. 435-436 ◽  
Author(s):  
J.A. Font ◽  
J.M. Marti ◽  
J.M. Ibáñez ◽  
E. Müller
Keyword(s):  
Numerical Simulations ◽  
Numerical Study ◽  
Supersonic Jets ◽  
Radio Sources ◽  
Riemann Solver ◽  
Relativistic Hydrodynamics ◽  
Two Dimensional ◽  
Relativistic Jets ◽  
Approximate Riemann Solver ◽  
Extragalactic Jets

Numerical simulations of supersonic jets are able to explain the structures observed in many VLA images of radio sources. The improvements achieved in classical simulations (see Hardee, these proceedings) are in contrast with the almost complete lack of relativistic simulations the reason being that numerical difficulties arise from the highly relativistic flows typical of extragalactic jets. For our study, we have developed a two-dimensional code which is based on (i) an explicit conservative differencing of the special relativistic hydrodynamics (SRH) equations and (ii) the use of an approximate Riemann solver (see Martí et al. 1995a,b and references therein).

scholarly journals An Exact Riemann Solver for Multicomponent Turbulent Flow

2000 ◽  
Vol 14 (2) ◽  
pp. 117-131 ◽  
Author(s):  
EMMANUELLE DECLERCQ ◽  
ALAIN FORESTIER ◽  
JEAN-MARC HÉRARD ◽  
XAVIER LOUIS ◽  
GÉRARD POISSANT
Keyword(s):  
Turbulent Flow ◽  
Riemann Solver ◽  
Exact Riemann Solver

scholarly journals On the development of a rotated-hybrid HLL/HLLC approximate Riemann solver for relativistic hydrodynamics

2020 ◽  
Vol 496 (2) ◽  
pp. 2493-2505
Author(s):  
Jamie F Townsend ◽  
László Könözsy ◽  
Karl W Jenkins
Keyword(s):  
Mach Reflection ◽  
Strong Shock ◽  
High Order ◽  
Numerical Dissipation ◽  
Test Cases ◽  
Riemann Solver ◽  
Relativistic Hydrodynamics ◽  
Robust Solution ◽  
Riemann Solvers ◽  
High Order Schemes

ABSTRACT This work presents the development of a rotated-hybrid Riemann solver for solving relativistic hydrodynamics (RHD) problems with the hybridization of the HLL and HLLC (or Rusanov and HLLC) approximate Riemann solvers. A standalone application of the HLLC Riemann solver can produce spurious numerical artefacts when it is employed in conjunction with Godunov-type high-order methods in the presence of discontinuities. It has been found that a rotated-hybrid Riemann solver with the proposed HLL/HLLC (Rusanov/HLLC) scheme could overcome the difficulty of the spurious numerical artefacts and presents a robust solution for the Carbuncle problem. The proposed rotated-hybrid Riemann solver provides sufficient numerical dissipation to capture the behaviour of strong shock waves for RHD. Therefore, in this work, we focus on two benchmark test cases (odd–even decoupling and double-Mach reflection problems) and investigate two astrophysical phenomena, the relativistic Richtmyer–Meshkov instability and the propagation of a relativistic jet. In all presented test cases, the Carbuncle problem is shown to be eliminated by employing the proposed rotated-hybrid Riemann solver. This strategy is problem-independent, straightforward to implement and provides a consistent robust numerical solution when combined with Godunov-type high-order schemes for RHD.

Extension and Comparative Study of AUSM-Family Schemes for Compressible Multiphase Flow Simulations

2014 ◽  
Vol 16 (3) ◽  
pp. 632-674 ◽  
Author(s):  
Keiichi Kitamura ◽  
Meng-Sing Liou ◽  
Chih-Hao Chang
Keyword(s):  
Phase Interface ◽  
Ideal Gas ◽  
Benchmark Problems ◽  
Riemann Solver ◽  
Model Concept ◽  
Flow Simulations ◽  
Dissipation Term ◽  
Compressible Multiphase Flow ◽  
Exact Riemann Solver ◽  
Special Case

AbstractSeveral recently developed AUSM-family numerical flux functions (SLAU, SLAU2, AUSMM+-up2, and AUSMPW+) have been successfully extended to compute compressible multiphase flows, based on the stratified flow model concept, by following two previous works: one by M.-S. Liou, C.-H. Chang, L. Nguyen, and T.G. Theofanous [AIAA J. 46:2345-2356, 2008], in which AUSM+-up was used entirely, and the other by C.-H. Chang, and M.-S. Liou [J. Comput. Phys. 225:840-873, 2007], in which the exact Riemann solver was combined into AUSM+-up at the phase interface. Through an extensive survey by comparing flux functions, the following are found: (1) AUSM+-up with dissipation parameters of Kp and Ku equal to 0.5 or greater, AUSMPW+, SLAU2, AUSM+-up2, and SLAU can be used to solve benchmark problems, including a shock/water-droplet interaction; (2) SLAU shows oscillatory behaviors [though not as catastrophic as those of AUSM+ (a special case of AUSM+-up with Kp = Ku = 0)] due to insufficient dissipation arising from its ideal-gas-based dissipation term; and (3) when combined with the exact Riemann solver, AUSM+-up (Kp = Ku = 1), SLAU2, and AUSMPW+ are applicable to more challenging problems with high pressure ratios.

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