Mathematical Sciences: Parallel Algorithms for Surface Water Flows and Transport

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Wheeler The investigator and her colleagues study scalable parallel algorithms for the solution of the hydrodynamic flow and transport equations. The mathematical model is based on the generalized wave-continuity equation for wave height, the non-conservative form of the momentum equations for velocity, and the advection-diffusion equation for transport. The numerical solution techniques are based on mixed and Galerkin finite element methods. For advection processes they study both characteristic and higher-order Godunov methods. These algorithms are implemented on parallel platforms, including clusters of workstations and massively parallel systems. Domain decomposition techniques are used to achieve parallelism. Once the codes are developed and validated, they are applied to bay and estuarine modeling and modeling of storm surges along the Gulf of Mexico. The objective of this research is to formulate, analyze and implement accurate and efficient parallel algorithms for modeling flow and transport in surface water environments. The impetus for this research is the need for state and federal agencies and private industry to understand the effects of tides on coastal regions and offshore structures, and to study the effects of industrial and municipal development on bays and estuaries. More specifically, this work has applications in several areas, including 1) calculating tidal ranges and surges caused by extreme storm events such as hurricanes in order to plan development in coastal areas and predict potential hazards from flooding; 2) modeling tidal fluctuations for those interested in capturing tidal energy for commercial purposes; 3) estimating forces on offshore structures; 4) predicting influence of dredging of intercoastal waterways or constructing breakwaters; 5) studying effects of pollution on bays and estuaries, including possible remediation strategies; and 6) allocating allowable discharges for municipalities in order to meet spec ific water quality objectives. The algorithms developed under this grant improve upon existing algorithms by effectively using massively parallel computers to increase resolution and reduce the computational time for a simulation. The code to be developed serves as paradigm for a new generation of software that takes advantage of the trend in high-performance computing toward massively parallel architectures.