Compressible Fluid Dynamics in Porous Media by the Boundary Element Method

Abstract

Over recent decades, fluid flows in porous media have been studied both experimentally and theoretically. Different numerical methods were used for obtaining the solutions of some transport phenomena in porous media, e.g. the finite-difference method (FDM), finite element method (FEM), finite volume method (FVM), as well as the boundary element method (BEM). The main comparative advantage of the BEM, the application of which requires the given partial differential equation to be mathematically transformed into the equivalent integral equation representation, which is later to be discretized over the discrete approximative methods is demonstrated in cases where this procedure results in boundary integral equations only, see Brebbia [2]. This turns out to be possible only for potential problems, e.g. inviscid fluid flow, heat conduction, etc. In general, the procedure results in boundary-domain integral equations and therefore several techniques were developed to extend the classical BEM, see Brebbia et al. [3]. The dual reciprocity boundary element method (DRBEM) represents one of the possibilities for transforming the domain integrals into a finite series of boundary integrals. The key point of the DRBEM is the approximation of the field in the domain by a set of global approximation functions and the subsequent representation of the domain integrals of these global functions by boundary integrals.