Numerical Boundary Conditions for Wave Propagation and FluidDynamics

波传播和流体动力学的数值边界条件

• 批准号: 9103197
• 负责人: Robert Higdon
• 金额: $ 3.88万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103197&HistoricalAwards=false
• 关键词: Numerical; Boundary; Conditions; Wave; Propagation

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.

首席研究员将研究涉及波传播和流体动力学问题的开放边界条件的各种问题。研究主题包括色散波的吸收边界条件、旋转参照系中浅水方程的开放边界条件以及弹性波动方程的速度-应力公式的吸收边界条件。这项工作的动机是，许多物理问题是在空间域上定义的，这些空间域要么是无界的，要么是如此之大，以至于在整个区域内计算数值解是不可行的。在这种情况下，截断域是必要的。然后，人们遇到了在人工计算边界上寻找边界条件的问题。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建模，包括大气和海洋的大尺度运动、地球内部的地震波和水面上的波浪。例如，假设一位海洋学家想要模拟海洋中的环流。一种可能性是计算分布在整个海洋上的网格点阵列的相关物理量。如果整个海洋都需要循环，这就是必须要做的。另一方面，如果流通只需要在相对较小的部分，如大陆架，那么上述过程就太昂贵了。相反，人们更愿意只在真正感兴趣的区域计算流通。在这样的计算中，区域的部分或全部边界是“开放”的，而不是物理的。告诉解在这样的边界处做什么是相当棘手的，边界条件的不正确选择可能严重破坏计算出的解。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对于使用地震方法寻找可能含有石油的地质结构的地球物理学家是有用的，而水波的开放边界条件对于研究波浪作用对海岸和近海结构的影响的工程师是有用的。