Integrated Analytical/Numerical Methods for Advanced Scientific Computing Applications

本研究涉及多尺度问题的数值方法的发展。本文提出将渐近方法与数值离散方法相结合的“助推器”或“广义误差修正”（GEM）方法应用于1)高雷诺数层流，2)不同时间尺度的时变流动，3)低普朗特数热对流，4)湍流输移建模。局部渐近性与整体GEM框架的结合以及并行计算的利用将使上述问题的求解效率至少提高一个数量级。

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.