The weighted average flux method applied to the Euler equations

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.