Mathematical Sciences: Study of Model Equations for Water Waves

[9410188] Chen研究员将研究各种描述水波在非线性色散介质中双向传播的Boussinesq系统。这个项目的主要目标是决定哪种方程组最适合于流体力学中物理问题的建模。研究者将从理论上和数值上研究这些系统，并将结果与实验室实验进行比较。研究者还将参与开发和实施一种有效的算法，通过数值积分完整的欧拉方程来模拟水波。这里得到的数值结果也将为验证Boussinesq系统提供一个来源。此外，研究者将继续研究最近发展的惯性多网格算法的思想。本文将从分岔理论的角度研究算法的动力学行为。研究者将研究由数值近似生成的分岔图，并将其与潜在连续问题的分岔图进行比较。在实践中，这意味着一次检查所有物理参数范围的数值方法。＊＊＊

9410188 Chen The investigator will study various Boussinesq systems which describe the two-way propagation of water waves in a nonlinear, dispersive media. The major goal for this project is to decide which system of equations is best suited for the modelling of physical problems in fluid mechanics. The investigator will study the systems both theoretically and numerically, and compare results with laboratory experiments. The investigator will also be involved in developing and implementing an efficient algorithm for the computer modelling of water waves through numerically integrating the full Euler's equations. The numerical results obtained here will also provide a source for the verification of Boussinesq systems. In addition, the investigator will continue research on the recently developed idea of Inertial Multigrid Algorithms. The dynamical behavior of the algorithms will be studied from the perspective of bifurcation theory. The investigator will study the bifurcation diagram generated by the numerical approximation and compare it with that of the underlying continuous problem. In practice, this means examining the numerical method for all range of the physical parameters at once. ***