Numerical integration of the Ostrovsky equation based on its geometric structures
Numerical integration of the Ostrovsky equation based on its geometric structures
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基于奥斯特洛夫斯基方程几何结构的数值积分
DOI：
10.1016/j.jcp.2012.02.027
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
T. Matsuo
中科院分区：
文献类型：
--
作者：
Y. Miyatake;T. Yaguchi;T. Matsuo
我们考虑Ostrovsky方程的结构保持数值方案，该方程描述了科里奥利力影响下的重力波。这个方程有两个相关的不变量：能量函数和L2范数。人们普遍认为，结构保持方法，如不变量保持和多辛积分通常产生定性更好的数值结果。在本文中，我们提出了这个方程的五个几何积分：能量保持和范数保持有限差分和Galerkin计划，和一个多辛积分的基础上新发现的多辛公式。数值比较表明，能量守恒差分格式比其它格式优越。
We consider structure preserving numerical schemes for the Ostrovsky equation, which describes gravity waves under the influence of Coriolis force. This equation has two associated invariants: an energy function and the L2norm. It is widely accepted that structure preserving methods such as invariants-preserving and multi-symplectic integrators generally yield qualitatively better numerical results. In this paper we propose five geometric integrators for this equation: energy-preserving and norm-preserving finite difference and Galerkin schemes, and a multi-symplectic integrator based on a newly found multi-symplectic formulation. A numerical comparison of these schemes is provided, which indicates that the energy-preserving finite difference schemes are more advantageous than the other schemes.