An Adaptive Finite Element Methodology for the High-Performance Computer Simulation of Multiphase Flow Processes.
Date of Award
Doctor of Philosophy (PhD)
John M. Tyler
A methodology has been developed for the computer simulation of multiphase flow processes in porous media. The solutions to the nonlinear equations describing these processes are approximated by Galerkin's method on the spatial dimensions and the finite difference method on the temporal dimension. Due to the transient nature of discontinuities in the spatial domain, dynamic mesh refinement (and unrefinement) techniques, based on the maintenance of a 1-irregular mesh, are employed on a two dimensional mesh to produce fine resolution in regions of activity and coarse resolution elsewhere. Our unique approach is tested by comparing computed results with data from laboratory experiments. The groundwork for extending this approach to three dimensional problems is laid in the development of a new finite element for use in 1-irregular adaptive schemes. We describe the development of this element, prove its correctness, and demonstrate its utility in a test problem. Finally, a three dimensional static-mesh version of the approach is distributed over a cluster of workstations, utilizing PVM for message passing. The repeated solution of large systems of equations dominates the computations, and is the focus of the effort in parallelization. Substructuring techniques are employed, allowing for efficient coarse-grained computations due to the distribution of expensive matrix operations over multiprocessors. An analysis of the performance characteristics of this approach is given, followed by a description of tests on a real-world problem.
Morton, Donald J. Jr, "An Adaptive Finite Element Methodology for the High-Performance Computer Simulation of Multiphase Flow Processes." (1994). LSU Historical Dissertations and Theses. 5819.