Title: A characteristic method for porous medium flow

Authors: Mohamed Al-Lawatia, Kaixin Wang, Aleksey S. Telyakovskiy, Hong Wang

Addresses: Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Sultanate of Oman. ' School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, China. ' Department of Mathematics and Statistics, University of Nevada, Reno, Nevada 89557, USA. ' Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA

Abstract: We present an efficient and accurate characteristic method for the solution of the unsteady-state advection-diffusion transport equations, which arise in the mathematical models for flow and transport processes in porous media. The advantages of this method include symmetrising the governing transport equation, treating boundary conditions naturally in the formulation, and conserving mass. Moreover, because of the Lagrangian nature of the algorithm used, the method generates accurate numerical solutions even when large time steps and coarse spatial grids are used in the simulation. Numerical experiments are presented to illustrate the performance of the method.

Keywords: characteristic methods; Eulerian–Lagrangian methods; ELM; compositional flow models; porous medium flow; unsteady state transport equations; advection-diffusion transport equations; simulation.

DOI: 10.1504/IJCSM.2007.016546

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.2/3/4, pp.467 - 479

Available online: 07 Jan 2008 *

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