U.S.-Mexico Cooperative Research: Development and Application of Numerical Techniques For Groundwater Simulation

该奖项将支持普林斯顿大学的George Pinder教授和墨西哥自治大学（UNAM）的Ismael Herrera教授之间的合作研究。研究人员打算开发数学工具，以便有效和准确地模拟地下水的流动和输送。更具体地说，他们将设计一个交替方向搭配的计算机代码，能够模拟地下水在地下多相流动和输送的运动，并可在并行处理器超级计算机上编程。此外，将开发基于总导数公式的最小二乘搭配算法，该算法将准确模拟具有陡峭锋面的污染物的运动。此外，研究人员计划研究边界元技术来模拟地下非水相流体的运动，并从泛函分析的角度对交替方向搭配算法进行理论分析。近十年来，人们在设计合适的数值方法以精确模拟地下水流动和输送模拟中锋面的传播方面做了许多努力。通过将墨西哥方面的理论专业知识与美国方面在地下流动和运输建模方面的实践经验相结合，拟议的工作将有助于提高我们对此类流动问题的理解。

This award will support collaborative research between Professor George Pinder of Princeton University and Professor Ismael Herrera of the Universidad Autonoma de Mexico (UNAM) in Mexico City, Mexico. The investigators intend to develop mathematical tools that allow the efficient and accurate simulation of groundwater flow and transport. More specifically, they will design an alternating direction collocation computer code, capable of simulating the movement of multiphase groundwater flow and transport in the subsurface, and programmable for a parallel processor supercomputer. Further, a least squares collocation algorithm will be developed, based upon a total derivative formulation, that will accurately simulate the movement of contaminants exhibiting steep fronts. In addition, the researchers plan to look at boundary element techniques to simulate the movement of non-acqueous phase fluids in the subsurface and carry out a theoretical analysis of the alternation direction collocation algorithm from a functional analysis point of view. Many efforts have been made over the last ten years in devising appropriate numerical methods that can accurately simulate the propagation of sharp fronts in groundwater flow and transport modeling. The proposed work will serve to advance our understanding of such flow problems by combining the theoretical expertise of the Mexican side with the practical experience of the U.S. side in subsurface flow and transport modeling.