scholarly journals An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows

2011 ◽  
Vol 235 (8) ◽  
pp. 2030-2040 ◽  
Author(s):  
F. Kerger ◽  
P. Archambeau ◽  
S. Erpicum ◽  
B.J. Dewals ◽  
M. Pirotton
Keyword(s):  
Riemann Solver ◽  
Godunov Scheme ◽  
Mixed Flows ◽  
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 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

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.

A linearized Riemann solver for the time-dependent Euler equations of gas dynamics

1991 ◽  
Vol 434 (1892) ◽  
pp. 683-693 ◽  
Keyword(s):  
Euler Equations ◽  
Gas Dynamics ◽  
Hyperbolic Conservation Laws ◽  
Weighted Average ◽  
Time Dependent ◽  
Test Problems ◽  
Riemann Solver ◽  
Equations Of Gas Dynamics ◽  
Exact Riemann Solver ◽  
Linearized Riemann Solver

The time-dependent Euler equations of gas dynamics are a set of nonlinear hyperbolic conservation laws that admit discontinuous solutions (e. g. shocks). In this paper we are concerned with Riemann-problem-based numerical methods for solving the general initial-value problem for these equations. We present an approximate, linearized Riemann solver for the time-dependent Euler equations. The solution is direct and involves few, and simple, arithmetic operations. The Riemann solver is then used, locally, in conjunction with the weighted average flux numerical method to solve the time-dependent Euler equations in one and two space dimensions with general initial data. For flows with shock waves of moderate strength the computed results are very accurate. For severe flow régimes we advocate the use of the present linearized Riemann solver in combination with the exact Riemann solver in an adaptive fashion. Numerical experiments demonstrate that such an approach can be very successful. One-dimensional and two-dimensional test problems show that the linearized Riemann solver is used in over 99% of the flow field producing net computing savings by a factor of about 2. A reliable and simple switching criterion is also presented. Results show that the adaptive approach effectively provides the resolution and robustness of the exact Riemann solver at the computing cost of the simple linearized Riemann solver. The relevance of the present methods concerns the numerical solution of multi-dimensional problems accurately and economically.

scholarly journals An improved exact Riemann solver for multi-dimensional relativistic flows

2003 ◽  
Vol 479 ◽  
pp. 199-219 ◽  
Author(s):  
LUCIANO REZZOLLA ◽  
OLINDO ZANOTTI ◽  
JOSE A. PONS
Keyword(s):  
Riemann Solver ◽  
Exact Riemann Solver
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