Numerical Methods for Layered Ocean Models

本项目涉及偏微分方程的数值解，应用于海洋环流的分层模式。 所处理的具体问题包括以下方面。 (1)开发将空间"B-网格“应用于具有消失层的分层模型的数值方法，并在这种情况下将该网格与" C-网格”进行比较。 这些网格中的每一个都是交错网格，其质量变量和速度分量被定义在不同的位置。 目前，B网格广泛用于z坐标模型，而分层模型更通常使用C网格。 在本项目中特别感兴趣的是在可变的海底地形附近的行为和可能产生的网格噪声。 这些问题已经干扰了以前尝试使用分层模型的B-网格，但B-网格仍然有吸引力的属性，值得考虑。 (2)比较不同的动量方程的数值离散化公式，并比较不同的对流方法求解质量和动量方程。 感兴趣的一个问题是离散系统内的非线性相互作用的性质。 数值方案的选择也受到同时传输多个标量场的需要的影响。这项工作的总体目的是改进用于海洋环流计算机模拟的算法。 海洋在全球气候系统中发挥着至关重要的作用，而要更好地了解这一系统，部分取决于对长期海洋环流的数值模拟。 研究者开发了一种改进的时间步进方法和相关算法，本项目代表了进一步的工作，以提高海洋环流数值模型中使用的算法的准确性，效率和可靠性的目标。 研究人员与实践海洋建模者有着广泛的联系，他们提供了宝贵的见解来帮助指导这项研究。

This project is concerned with the numerical solution of partial differential equations, as applied to layered models of ocean circulation. Particular issues that are addressed include the following. (1) Develop numerical methods for applying the spatial ``B-grid'' to layered models with vanishing layers, and compare this grid to the ``C-grid'' in such situations. Each of these grids is a staggered grid for which the mass variables and velocity components are defined at different locations. Presently, the B-grid is widely used in z-coordinate models, whereas layered models more typically use the C-grid. Of particular interest in the present project are behavior near variable bottom topography and the possible generation of grid noise. These issues have interfered with previous attempts to use the B-grid with layered models, but the B-grid nevertheless has attractive properties that warrant consideration. (2) Compare different formulations of the momentum equation for numerical discretization, and compare different advection methods for solving the equations for mass and momentum. One issue of interest is the nature of the nonlinear interactions within the discrete system. The choice of numerical scheme is also influenced by the need to transport multiple scalar fields simultaneously.The overall purpose of this work is to improve the algorithms that are used in computer simulations of ocean circulation. The ocean plays a crucial role in the global climate system, and a better understanding of that system relies in part on numerical simulations of the ocean's circulation over long periods of time. The investigator has developed an improved time-stepping method and related algorithms, and the present project represents further work towards the goal of improving the accuracy, efficiency, and reliability of the algorithms that are used in numerical models of ocean circulation. The investigator has extensive contacts with practicing ocean modelers who provide valuable insights to help guide this research.