A Two-Stage Fourth Order Time-Accurate Discretization for Lax-Wendroff Type Flow Solvers I. Hyperbolic Conservation Laws
A Two-Stage Fourth Order Time-Accurate Discretization for Lax-Wendroff Type Flow Solvers I. Hyperbolic Conservation Laws
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DOI：
10.1137/15m1052512
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发表时间：
2015-12
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通讯作者：
Jiequan Li;Zhifang Du
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文献类型：
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作者：
Jiequan Li;Zhifang Du
在本文中，我们发展了一种新的两阶段四阶时间精确离散的时间依赖流问题，特别是双曲守恒律。与将一阶Riemann解算器作为构建块的经典Runge-Kutta（R-K）时间离散不同，当前方法仅与Lax-Wendroff（L-W）类型格式作为构建块相关。因此，可以构建两阶段程序来实现四阶时间精度，而不是使用成熟的R-K方法的四阶段。以广义Riemann问题（GRP）求解器作为L-W型格式的代表，构造了一个两步四阶格式。
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.