Some Applications of the Fundamental Solution Method for Modelling Fluif Flow in Porous Media

Abstract

The fundamental solution method is a meshless approach for the numerical solution of partial differential equations. Its implementation combines free Green functions, a generalization of image’s method, the singular value decomposition, and a boundary collocations method to produce a very simple algorithm for the simulation of some problems in science and engineering. A review of its adaptation to the solution of three classical problems for fluid flow in porous media is presented. These problems are: the tracer flow in a reservoir, the transient pressure distribution in an aquifer, and the computation of pressure and streamlines in a reservoir with thin geological barriers. The analysis of the results shows that the fundamental solution method is a new numerical alternative for the simulation of simple reservoirs or groundwater flow problems.