Mathematical Sciences: Study of Model Equations for Water Waves

点击翻译按钮获取中文摘要

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. ***