6 - Computational Methods in Fluid Flow

Abstract

This chapter discusses computational methods in fluid flow. Computational methods are an important tool in predicting the response of heterogeneous geological systems to coupled or uncoupled flow, transport, and deformation processes. As a domain method, elements must be distributed throughout the body of interest and the dependent variables defined at nodal points. Extensive meshing and the large number of resulting equations mandated by the domain-type methods can be circumvented by certain integral techniques. For certain classes of linear problems, boundary element methods are particularly powerful. The competing integral and domain solution techniques are largely complementary. Domain-type methods are unmatched in their ability to represent complex-coupled and nonlinear phenomena, while integral techniques are ideally suited to describe accurately linear, but volumetrically extensive, far-field of infinite body problems. Thus, the procedures can be used in isolation or in a coupled format to extract the most useful features from each. The behavior of the dual porosity continuum is described by the interaction of the basic components, namely, the porous medium and the surrounding fracture system. Irrespective of the particular choice of solution technique, computational methods provide a powerful tool in the quantification of flow and transport phenomena in rock mechanics.