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.
