HR: 1340h
AN: H33F-0526    [Abstracts]
TI: Numerical Advances in the Modeling of Highly Heterogeneous Domains Using the Analytic Element Method
AU: * Bandilla, K W
EM: bandilla@eng.buffalo.edu
AF: University at Buffalo, Department of Civil, Structural, and Environmental Engineering 207 Jarvis Hall, Buffalo, NY 14260-4400 United States
AU: Suribhatla, R M
EM: rms29@buffalo.edu
AF: University at Buffalo, Department of Civil, Structural, and Environmental Engineering 207 Jarvis Hall, Buffalo, NY 14260-4400 United States
AU: Jankovi\'{c}, I
EM: ijankovi@buffalo.edu
AF: University at Buffalo, Department of Civil, Structural, and Environmental Engineering 207 Jarvis Hall, Buffalo, NY 14260-4400 United States
AB: The Analytic Element Method (AEM) is an alternative to Finite Element and Finite Difference Methods for solving subsurface flow and transport problems in highly heterogeneous domains. Each hydrogeologic element (e.g. a zone where conductivity differs from the surrounding conductivity, a well, a river, etc.) in the domain of interest is represented by an analytic function. In order to solve the flow problem, the coefficients of the analytic function for each element must be computed so as to satisfy the boundary conditions. For the iterative approach used in this presentation, most of the computational effort is spent on computing the interactions between elements. These interactions are reflected in the element coefficients. Two approaches that can greatly reduce the run-time are examined in this presentation: the superblock approach and the parallel processing approach. The superblock approach groups elements into blocks, and treats each group as a single element while computing the influence of the group's elements on elements that are far from the group. Several superblock formulations exist. For example, the superblocks can be arranged using a Quad-Tree approach to further reduce the computational effort. Two superblock formulations will be examined. Parallel processing also reduces the time needed for solving the flow problem. The computations of the element coefficients are carried out separately for each element during a given step. Interactions are resolved using an iterative algorithm. The elements are hence divided up among many processors, so that a large number of element coefficients can be computed at the same time. The processors only need to communicate the new element coefficients at the end of each iterative step. This enhances the efficiency and the elegance of the approach. The two approaches described above are examined separately and in combination on a set of test problems containing a large number of circular inhomogeneities. Performance and efficiency are evaluated using a set of numerical simulations of flow in highly heterogeneous formations. The results show that as many as 250,000 2D inhomogeneities (and 100,000 3D inhomogeneities) can be simulated regardless of the packing densities and the heterogeneity levels. Variances of log-conductivity up to 10 can be analyzed. In addition to circular (2D) and spherical (3D) shapes the methodology was applied to other shapes.
DE: 3210 Modeling
DE: 3230 Numerical solutions
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting