Weighted average flux method and flux limiters for the numerical simulation of shock waves in rigid porous media

2002 ◽  
Vol 40 (9) ◽  
pp. 1187-1207 ◽  
Author(s):  
R. Torrens ◽  
L. C. Wrobel
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Shock Waves ◽  
Weighted Average ◽  
Flux Method ◽  
Average Flux ◽  
Flux Limiters

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.

The weighted average flux method applied to the Euler equations

1992 ◽  
Vol 341 (1662) ◽  
pp. 499-530 ◽  
Keyword(s):  
Euler Equations ◽  
Gas Dynamics ◽  
Hyperbolic Conservation Laws ◽  
Weighted Average ◽  
Two Dimensions ◽  
Test Problems ◽  
Flux Method ◽  
Hyperbolic Conservation ◽  
Equations Of Gas Dynamics ◽  
Average Flux

The weighted average flux method (WAF) for general hyperbolic conservation laws was formulated by Toro. Here the method is specialized to the time-dependent Euler equations of gas dynamics. Several improvements to the technique are presented. These have resulted from experience obtained from applying WAF to a variety of realistic problems. A hierarchy of solutions to the relevant Riemann problem, ranging from very simple approximations to the exact solution, are presented. Their performance in the WAF method for several test problems in one and two dimensions is assessed.

Sign in / Sign up

Export Citation Format

Share Document