Mathematical Sciences: Numerical Methods for Large-Scale Ocean Modeling

Higdon 研究人员研究描述大规模海洋环流的偏微分方程的数值解。 研究的主要课题是控制方程的算子分裂。 这些方程承认波速有很大的变化幅度，这种情况下产生严重的问题，数值算法的稳定性和效率。 解决这些问题的一种常见方法是将快动力学和慢动力学分解为单独的子问题。 快速运动基本上与深度无关，尝试用二维方程系统来模拟这些运动是很自然的。 然后用三维系统模拟慢动作。 然而，如果分裂是不精确的，那么假定模拟慢运动的方程实际上可能在某种程度上承认快运动。 然后出现的可能性，这些快速运动可能会导致计算算法中的数值不稳定性。 这个项目的主要目标是开发一个稳定的，高效的，准确的算子分裂的控制方程。 次要目标是开发有限区域模型的开放边界条件，并研究空间离散化的高阶差分方法。 当今科学界面临的主要挑战之一是获得多年来全球海洋环流的高分辨率计算机模拟。 这种模拟非常有趣，因为海洋是地球气候系统的重要组成部分，因此对可能的全球变化的研究必须包括对海洋作用的仔细检查。 例如，海洋有很大的能力来输送热能;这种输送部分是由于主要海流系统的大量输送，部分是由于海流脱落的小尺度涡旋引起的混合。 关于这些过程的全面数据很难收集，而且似乎准确的 要了解地球的气候系统，就需要根据海洋环流的涡旋解析模型进行数值模拟。 这种模拟将提出巨大的计算需求。 该项目的目标是为这些计算开发合适的数值方法。 这项工作是与俄勒冈州州立大学大气和海洋科学学院物理海洋学建模小组成员合作进行的。

Higdon The investigator studies the numerical solution of partial differential equations that describe large-scale ocean circulation. The main topic of investigation is operator splitting for the governing equations. These equations admit wave velocities having widely varying magnitudes, and this situation creates serious problems with the stability and efficiency of numerical algorithms. One common approach to resolving these problems is to split the fast and slow dynamics into separate subproblems. The fast motions are essentially independent of depth, and it is natural to try to model these motions with a two-dimensional system of equations. The slow motions would then be modeled with a three-dimensional system. However, if the splitting is inexact, then the equations that supposedly model the slow motions may actually admit fast motions, to some degree. There then arises the possibility that these fast motions might cause numerical instabilities in the computational algorithm. The main goal of this project is to develop a stable, efficient, and accurate operator splitting for the governing equations. Secondary goals are to develop open boundary conditions for limited-area models and to examine higher-order difference methods for spatial discretizations. One of the major scientific challenges of the present day is to obtain high-resolution computer simulations of global ocean circulation over periods of many years. Such simulations are of great interest because the ocean is a crucial component of the earth's climate system, so studies of possible global change must include a careful examination of the role of the ocean. For example, the ocean has a great capacity to transport heat energy; part of this transport is due to bulk transport by major current systems, and part is due to mixing caused by smaller-scale eddies that are shed from currents. Comprehensive data on these processes are difficult to collect, and it appears that an accurate understanding of the earth's climate system will require numerical simulations based on an eddy-resolving model of the general circulation of the ocean. Such simulations will present great computational demands. The goal of this project is to contribute to the development of suitable numerical methods for these computations. This work is being performed in collaboration with members of the physical oceanography modeling group in the College of Atmospheric and Oceanic Sciences at Oregon State University.