A comparative study of bi-directional Whitham systems
A comparative study of bi-directional Whitham systems
复制标题
双向Whitham系统的比较研究
DOI：
10.1016/j.apnum.2018.09.016
复制
发表时间：
2019
影响因子：
2.8
通讯作者：
H. Kalisch
中科院分区：
文献类型：
--
作者：
E. Dinvay;D. Dutykh;H. Kalisch
1967年，Whitham提出了一个简化的表面水波模型，该模型结合了全欧拉方程的全线性色散关系和弱线性近似。方程，他假设这是现在所谓的惠瑟姆方程最近已扩展到一个系统的方程允许双向传播的表面波。已经提出了许多不同的双向系统，即使从建模的角度来看它们是相似的，这些系统具有非常不同的数学性质。在当前的工作中，我们回顾了一些现有的完全色散系统，例如在[1]，[4]，[9]，[17]，[22]，[23]中发现的。我们使用最先进的数值工具，试图了解这些系统的初值问题的解的存在性和稳定性。我们还提出了一个新的系统，这是哈密尔顿和半线性。新的系统表现良好，无论是在近似完整的欧拉系统，以及关于适定性属性。
In 1967, Whitham proposed a simplified surface water-wave model which combined the full linear dispersion relation of the full Euler equations with a weakly linear approximation. The equation he postulated which is now called the Whitham equation has recently been extended to a system of equations allowing for bi-directional propagation of surface waves. A number of different two-way systems have been put forward, and even though they are similar from a modeling point of view, these systems have very different mathematical properties.In the current work, we review some of the existing fully dispersive systems, such as found in [1], [4], [9], [17], [22], [23]. We use state-of-the-art numerical tools to try to understand existence and stability of solutions to the initial-value problem associated to these systems. We also put forward a new system which is Hamiltonian and semi-linear. The new system is shown to perform well both with regard to approximating the full Euler system, and with regard to well posedness properties.