Multiscale Computation and Modeling of Flows in Strongly Heterogeneous Porous Media
Thursday, January 10, 2002 - 11:00am - 12:00pm
Many problems of fundamental and practical importance contain multiple scale solutions. Direct numerical simulations of these multiscale problems are extremely difficult due to the range of length scales in the underlying physical problems. Here, we introduce a multiscale finite element method for computing flow transport in strongly heterogeneous porous media which contain many spatial scales. The method is designed to capture the large scale behavior of the solution without resolving all the small scale features. This is accomplished by constructing the multiscale finite element base functions that incorporate local microstructures of the differential operator. By using a novel over-sampling technique, we can reconstruct small scale velocity locally by using the multiscale bases. This property is used to develop a robust scale-up model for flows through heterogeneous porous media. To develop a coarse grid model for multi-phase flow, we propose to combine grid adaptivity with multiscale modeling. We also develop a new class of numerical methods for stochastic PDEs which can be used to compute two-point correlation functions and high order statitsical quantites more efficiently than the traditional Monte-Carlo method.