A TWO-STAGE FOURTH ORDER TIME-ACCURATE DISCRETIZATION FOR LAX WENDROFF TYPE FLOW SOLVERS I. HYPERBOLIC CONSERVATION LAWS

In this paper we develop a novel two-stage fourth order time-accurate discretization for time-dependent flow problems, particularly for hyperbolic conservation laws. Different from the classical Runge Kutta (R K) temporal discretization for first order Riemann solvers as building blocks, the current approach is solely associated with Lax-Wendroff (L-W) type schemes as the building blocks. As a result, a two-stage procedure can be constructed to achieve a fourth order temporal accuracy, rather than using the well-developed four-stage procedure for R K methods. The generalized Riemann problem (GRP) solver is taken as a representative of L-W type schemes for the construction of a two-stage fourth order scheme.