Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods
Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods
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DOI：
10.1016/s0378-4754(02)00179-9
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发表时间：
2003-02
期刊：
影响因子：
--
通讯作者：
R. Spiteri;Steven J. Ruuth
中科院分区：
文献类型：
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作者：
R. Spiteri;Steven J. Ruuth
强稳定性保持（SSP）时间离散方法（也称为总变差减小或TVD方法）是模拟具有间断或激波解的偏微分方程的流行和有效的算法。最佳SSP龙格库塔（SSPRK）计划以前已经发现的方法与多达五个阶段和多达四阶。在本文中，我们提出了新的最优四阶SSPRK计划与温和的存储要求和多达八个阶段。我们发现，这些计划最终是更有效的比已知的四阶SSPRK计划，因为在允许的时间步长的增加超过抵消增加的计算费用每一步。我们证明了这些效率对标量守恒律。
Strong-stability-preserving (SSP) time discretization methods (also known as total-variation-diminishing or TVD methods) are popular and effective algorithms for the simulation of partial differential equations having discontinuous or shock-like solutions. Optimal SSP Runge–Kutta (SSPRK) schemes have been previously found for methods with up to five stages and up to fourth order. In this paper, we present new optimal fourth-order SSPRK schemes with mild storage requirements and up to eight stages. We find that these schemes are ultimately more efficient than the known fourth-order SSPRK schemes because the increase in the allowable time-step more than offsets the added computational expense per step. We demonstrate these efficiencies on a pair of scalar conservation laws.