论文标题
Serre-Green-Naghdi方程和完全分散的对应物的数值研究
Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart
论文作者
论文摘要
我们对serre-green-naghdi（SGN）方程进行数字实验，并在维度1中进行完全分散的“ Whitham-Green-Naghdi”（WGN）对应物。特别是，WGN方程的单个波浪解决方案是构建的，并且它们的稳定性是稳定性的，以及它们的稳定性，以及Sgne equal equantions的透明度。此外，研究了调制振荡的出现以及在各种情况下进行解决方案爆炸的可能性。 我们认为，一种基于傅立叶光谱方法与Krylov子空间迭代技术GMRE的简单数值方案，以解决椭圆问题，并及时解决第四阶显式runge-kutta方案，甚至可以有效地解决计算上的挑战性问题。
We perform numerical experiments on the Serre-Green-Naghdi (SGN) equations and a fully dispersive "Whitham-Green-Naghdi" (WGN) counterpart in dimension 1. In particular, solitary wave solutions of the WGN equations are constructed and their stability, along with the explicit ones of the SGN equations, is studied. Additionally, the emergence of modulated oscillations and the possibility of a blow-up of solutions in various situations is investigated. We argue that a simple numerical scheme based on a Fourier spectral method combined with the Krylov subspace iterative technique GMRES to address the elliptic problem and a fourth order explicit Runge-Kutta scheme in time allows to address efficiently even computationally challenging problems.
