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

Abstract

SUMMARYThe one-dimensional ow ÿeld generated by the passage of a shock wave in a rigid, thermoelastic porous foam has been simulated using a two-phase mathematical model. The work presented here makes use of the weighted average ux method to solve the system of six equations that govern the problem. Spurious oscillations are eliminated through the application of total variation diminishing limiting methods. Four di erent limiters were tested: van Leer, SuperA, MinA and van Albada. Numerical tests were carried out to verify the performance of each ux limiter in terms of accuracy. The results were compared to analytical and previously obtained data to assess the performance of the mathematical model. Excellent agreement was obtained.

On the propagation of a normal shock wave through a layer of incompressible porous material

“…This concept is consistent with the phenomenological model of Levy et al (1993b). The primary reason the numerical results over predict the experimental results lies in some of the assumptions made to simplify the system of governing equations in order to produce the numerical model (Torrens and Wrobel (2002)). Of the assumptions made, the two of most interest are (a) the fluid is ideal and therefore does not experience any viscous dissipative forces and (b) the energy processes in the fluid and the solid are reversible.…”

“…The full system of macroscopic balance equations, obtained under a set of simplifying assumptions discussed by Levy et al (1996) and Torrens and Wrobel (2002), along with the constitutive relationships for stress and strain in the solid matrix and the equation of state for the gas, are given in the form:…”

“…This results in a constant Jacobian matrix, à . The eigenvalues, eigenvectors and wave strengths of à were found symbolically using Mathematica, and are presented in full by Torrens and Wrobel (2002).…”

“…The grid sensitivity of the present numerical scheme was examined in Torrens and Wrobel (2002). To effectively model a 1.6 metre long domain, occupied entirely by porous medium, at least 400 computational nodes were required.…”

“…Numerical solutions were obtained based on the experimental test cases given in Levy et al (1993). Torrens and Wrobel (2002) presented a numerical model, based on the application of the Weighted Average Flux (WAF) method of Toro (1992), to the theoretical model of shock wave flow in porous medium discussed in Levy et al (1996). The numerical model was used to generate solutions for a shock tube problem where the domain was occupied entirely by a porous medium.…”