An iterative method to solve a regularized model for strongly nonlinear long internal waves
An iterative method to solve a regularized model for strongly nonlinear long internal waves
复制标题
求解强非线性长内波正则化模型的迭代方法
DOI：
10.1016/j.jcp.2010.11.049
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Tae
中科院分区：
文献类型：
--
作者：
W. Choi;Arnaud Goullet;Tae
我们提出了一种简单的迭代方案来数值求解描述两层不同密度的界面的大振幅运动的正则内波模型。与Miyata[10]和Choi and Camassa[2]等原始的强非线性内波模型相比，本文采用的正则化模型抑制了界面上速度跳变引起的剪切失稳，但由于上下两层之间的耦合更为复杂，在对一组非线性演化方程进行时间积分后，必须在每一个时间步都求解一个附加的耦合线性方程组。因此，需要一种有效的数值格式。在我们的迭代方案中，线性系统是解耦的，并且要求简单的常系数线性算子被反转。通过线性分析表明，该方案在迭代参数选择最优的情况下收敛速度快。在证明了迭代格式对模型问题的有效性之后，将迭代格式应用于求解单个内孤立波传播和两个不同波幅的孤立波正面碰撞的正则内波模型的伪谱方法。
We present a simple iterative scheme to solve numerically a regularized internal wave model describing the large amplitude motion of the interface between two layers of different densities. Compared with the original strongly nonlinear internal wave model of Miyata [10] and Choi and Camassa [2], the regularized model adopted here suppresses shear instability associated with a velocity jump across the interface, but the coupling between the upper and lower layers is more complicated so that an additional system of coupled linear equations must be solved at every time step after a set of nonlinear evolution equations are integrated in time. Therefore, an efficient numerical scheme is desirable. In our iterative scheme, the linear system is decoupled and simple linear operators with constant coefficients are required to be inverted. Through linear analysis, it is shown that the scheme converges fast with an optimum choice of iteration parameters. After demonstrating its effectiveness for a model problem, the iterative scheme is applied to solve the regularized internal wave model using a pseudo-spectral method for the propagation of a single internal solitary wave and the head-on collision between two solitary waves of different wave amplitudes.