Integrated Analytical/Numerical Methods for Advanced Scientific Computing Applications

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This research is concerned with the development of numerical methods for multiple scales problems. It is proposed to apply the "booster" or "generalized error modification" (GEM) method which combines an asymptotic apporach with numerical discretization methods on 1) laminar flows at high Reynolds numbers, 2) time dependent flows with disparate time scales, 3) low-Prandtl number thermal convection, and 4) turbulent transport modeling. The marriage of local asymptotics with the overall GEM framework, and exploitation of parallel computing will improve the efficiency of solution of the aforementioned problems by at least an order of magnitude.