An Investigation of Flux-limiting and Non-Linear Solution Techniques for Efficient Simulation of Transport in Porous Media
by
Mohammad Awad
School of Mathematical Sciences, Queensland University of Technology
Coauthors: Ian Turner (Queensland University of Technology)

The equations that govern the flow of liquids in porous media are ubiquitous in science and engineering. For example, the governing equations find application in fields as diverse as drying, ground water flow, contamination and petroleum reservoir engineering. Typically, the conservation laws that are encountered are highly non-linear and have steep fronts that require resolution in time. It is one of the aims of this work to analyse the use of higher order spatial weighting schemes and temporal methods for reducing numerical dispersion. Another important ingredient in the development of an efficient simulator is the treatment of the non-linear system that results from the discrete analogue of the conservation law. In this work a vertex-centered finite volume method has been used for discretising a representative conservation law in one-dimension and a variety of non-linear iterative methods, including a globally convergent Newton's method and a quasi-Newton method, will be scrutinised. Two case studies have been chosen to highlight the performance of the chosen numerical techniques. At first, the focus will be on the accuracy and efficiency of the spatial weighting methods for a linear advection-dispersion equation and then, a two-phase flow problem will be analysed to gauge the performance of the non-linear solvers. In both cases, comparisons with exact solutions will be provided.

Date received: July 29, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-74.