Numerical Boundary Conditions for Wave Propagation and FluidDynamics

首席研究员将研究各种问题 波浪问题的开边界条件 传播和流体动力学。调查的主题 包括色散波吸收边界条件，开 浅水方程的边界条件 参考坐标系和吸收边界条件， 弹性波方程的速度-应力公式。 这 工作的动机是，许多身体问题， 定义在空间域上，要么是无界的，要么是无界的， 大到不可能计算数值解 整个地区 在这种情况下，有必要 截断域。 然后，人们会遇到这样的问题： 寻找边界条件强加在人工 计算边界 这种边界条件的发展是主题 of this research研究. 这项工作有望应用于 几种物理现象的计算机建模， 包括大气和海洋的大尺度运动， 地球内部的地震波， 水 例如，假设一个海洋学家想建立一个模型， 海洋中的环流 一种可能性是计算 网格点阵列上的相关物理量 分布在整个海洋。 如果需要循环 为了整个海洋，这是必须要做的。 另 一方面，如果流通只需要在一个相对较小的 部分，如大陆架，则上述程序 太昂贵了 相反，人们更愿意计算 只在真实的兴趣区域上流通。以这样的 计算时，该区域部分或全部由 这是一个“开放”的边界，而不是物理边界。 说的 在这样的边界上做什么是相当棘手的， 边界条件的错误选择会严重破坏 计算的解决方案。本研究的目的是 开发有效的物理开放边界条件 上述情况。 地震开边界条件 波将是有用的地震学家谁使用地震方法， 寻找可能含有石油的地质结构， 水波的开放边界条件将有助于 研究波浪作用对沿海和沿海地区影响的工程师， 海上结构物。

The principal investigator will study various questions involving open boundary conditions for problems in wave propagation and fluid dynamics. The topics of investigation include absorbing boundary conditions for dispersive waves, open boundary conditions for the shallow water equations in a rotating reference frame, and absorbing boundary conditions for the velocity-stress formulation of the elastic wave equation. This work is motivated by the fact that many physical problems are defined on spatial domains that either are unbounded or are so large that it is not feasible to compute numerical solutions over the entire region. In such situations, it is necessary to truncate the domain. One then encounters the problem of finding boundary conditions to impose at the artificial computational boundary. The development of such boundary conditions is the subject of this research. This work is expected to have applications to computer modeling of several kinds of physical phenomena, including large scale motions of the atmosphere and oceans, seismic waves within the earth, and waves on the surface of water. For example, suppose that an oceanographer wants to model the circulation in an ocean. One possibility is to compute the relevant physical quantities on an array of grid points distributed over the entire ocean. If the circulation is needed for the entire ocean, this is what must be done. On the other hand, if the circulation is needed only on a relatively small portion, such as the continental shelf, then the above procedure is far too costly. Instead, one would prefer to compute the circulation only on the region of real interest. In such a computation, the region is bounded partly or entirely by a boundary that is "open" instead of physical. Telling the solution what to do at such a boundary is rather tricky, and an incorrect choice of boundary conditions can seriously corrupt the solution that is computed. The goal of the present research is to develop effective open boundary conditions for the physical situations mentioned above. Open boundary conditions for seismic waves would be useful to geophysicists who use seismic methods to search for geologic structures that could contain petroleum, and open boundary conditions for water waves would be useful to engineers who study the effects of wave actions on coastal and offshore structures.