Partitioning of Coupled Flow Problems

研究者和他的学生在计算流体动力学和数值分析方面进行研究，对耦合流动问题的模块化解耦算法进行开发、分析和验证。研究涉及三个相关问题：基于非线性滤波的湍流模型、基于快慢波分裂和时间滤波的地球物理模拟方法以及地下水-地表水耦合流动。第一个问题的关键思想是使用简单的湍流模型，并通过一个不耦合的模块化过滤步骤来调整/改进模型。这种方法允许将现代模型轻松地引入到遗留代码中。为提高模型精度提供了一条清晰的途径。第二个研究问题是对地球物理流动模拟中最常用的工具（所谓的）基于快慢波分裂和时间滤波的CNLF方法进行数学上的合理理解。第三个问题是开发地下水-地表水耦合流动和污染物运移问题的分区方法。所研究的方法将允许通过连续调用为每个物理子过程优化的单独程序来解决实际参数值的耦合进化问题。这三个项目处理的是非常重要和长期困难的问题。这些问题被选择为那些需要在算法和数值分析方面取得根本性突破才能向前迈出一步的问题。每个项目都涉及到一个或多个新颖想法的发展，这些想法有望突破严重限制当前方法的基本困难。多物理问题的多速率、分区方法的总体项目处于分析技术、计算机硬件能力和人类程序员能力的局限性的十字路口。第一个研究主题是在遗留代码中实现新的湍流模型，并随着湍流知识的扩展而提高它们的准确性——这是许多工业研究小组的中心问题。二是了解和改进大气和海洋代码中的主要工具。这在全球变化估计和污染扩散估计中具有重要意义。第三是发展污染物进出地表水和地下水的耦合输送方法。这是一个与工业和农业过程的污染物控制和清理直接相关的当前问题。

The investigator and his students conduct research in computational fluid dynamics and numerical analysis on the development, analysis and validation of modular, uncoupling algorithms for coupled flow problems. The research involves three related problems: nonlinear filter based turbulence models, geophysical simulation methods based on fast-slow wave splitting and time filters and coupled groundwater-surface water flows. The key idea of the first problem is to use simple turbulence models and adapt / refine the models through an uncoupled, modular filter step. This approach allows easy introduction of modern models into legacy codes. It also gives a clear path for improvement of model accuracy. The second research problem is to develop a mathematically sound understanding of the most commonly used tools in geophysical flow simulations of the (so called) CNLF method based on fast-slow wave splitting with time filtering. The third problem is to develop partitioned methods for coupled groundwater-surface water flow and contaminant transport problems. The methods studied will allow the solution of coupled, evolutionary problems for realistic parameter values by successive calls to separate programs optimized for each physical sub-process. The three projects treat problems of great importance and long-standing difficulty. The problems are selected to be ones where a fundamental breakthrough is necessary in both algorithms and numerical analysis to take a step forward. Each project involves development of one or more novel ideas that have promise to breakthrough a fundamental difficulty severely limiting current methods. The overarching project of multi-rate, partitioned methods for multi-physics problems lies at the crossroads where the limitations of analytical technique, computer hardware capabilities and human programmer abilities come together. The first research theme concerns implementation of new turbulence models in legacy codes and increasing their accuracy as knowledge of turbulent flows expands - a central problem in many industrial research groups. The second is to understand and improve the major tool in atmosphere and ocean codes. This is of great importance in global change estimation and in estimation of pollution dispersal. The third is to develop methods for coupled transport of contaminants to and from surface water and groundwater. This is a problem of current interest directly related to control of contaminants and cleanup from industrial and agricultural processes.