A unified Riemann-probiem-based extension of the Warming–Beam and Lax–Wendroff schemes

A unified, Riemann-problem-based extension of the Warming–Beam and Lax- Wendroff schemes for nonlinear systems of hyperbolic conservation laws is presented. This is achieved by employing the weighted average flux (WAF) approach with the numerical flux given by a space–time integral average of the solution of local Riemann problems. The local wave structure dictates switching between schemes automatically with no need for special conservative switching operators. The resulting Godunov-type scheme has CFL-number 2 stability restriction and when used in conjunction with Riemann-solver adaption procedures is significantly more efficient than Riemann-problem-based methods currently in use.