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arXiv · 1512.03664

A Two-Stage Fourth Order Time-Accurate Discretization for Lax-Wendroff Type Flow Solvers. I. Hyperbolic Conservation Laws

Jiequan Li·Zhifang Du
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Abstract

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.

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Jiequan Li, Zhifang Du. 2015-12-11. A Two-Stage Fourth Order Time-Accurate Discretization for Lax-Wendroff Type Flow Solvers. I. Hyperbolic Conservation Laws. https://arxiv.org/abs/1512.03664

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