Numerical Boundary Conditions for Wave Propagation and FluidDynamics

首席研究员将研究波传播和流体动力学中涉及开放边界条件的各种问题。研究内容包括色散波的吸收边界条件、旋转坐标系中浅水方程的开放边界条件和弹性波方程速度-应力方程的吸收边界条件。这项工作的动机是这样一个事实，即许多物理问题定义在空间域上，这些空间域要么是无界的，要么是太大的，以至于不可能计算整个区域的数值解。在这种情况下，有必要截断域。然后，人们遇到了寻找边界条件以强加于人工计算边界的问题。这种边界条件的发展是本研究的主题。这项工作有望应用于几种物理现象的计算机模拟，包括大气和海洋的大范围运动、地球内的地震波和水面上的波。例如，假设一位海洋学家想要模拟海洋中的环流。一种可能性是在分布在整个海洋上的一组网格点上计算相关的物理量。如果整个海洋都需要循环，这就是必须要做的。另一方面，如果只需要在相对较小的部分进行流通，如大陆架，则上述程序成本太高。相反，人们更愿意只计算实际感兴趣的区域的发行量。在这样的计算中，区域的边界部分或全部由一个“开放”的边界而不是物理边界来界定。告诉解在这样的边界上做什么是相当棘手的，并且不正确的边界条件选择可能会严重破坏所计算的解。本研究的目的是为上述物理情况开发有效的开放边界条件。地震波的开放边界条件将有助于地球物理学家使用地震方法寻找可能含有石油的地质构造，而水波的开放边界条件将有助于研究波浪作用对海岸和近海结构物的影响的工程师。

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.