A Two-Stage Fourth Order Time-Accurate Discretization for Lax-Wendroff Type Flow Solvers. I. Hyperbolic Conservation Laws
It provides a more efficient temporal discretization for flow solvers, reducing computational cost while maintaining high accuracy.
This paper develops a two-stage fourth-order time-accurate discretization for hyperbolic conservation laws using Lax-Wendroff type schemes, achieving fourth-order temporal accuracy with only two stages instead of the four required by Runge-Kutta methods.
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 well-developed four stages 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.