Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media

Abstract

We consider a nite volume method for ow simulations in an anisotropic porous medium in the presence of a well. The hydraulic head varies logarithmically and its gradient changes rapidly in the well vicinity. Thus, the use of standard numerical schemes results in a completely wrong total well ux and an inaccurate hydraulic head. In this article we propose two nite volume methods to model the well singularity in an anisotropic medium. The rst method signi cantly reduces the total well ux error, but the hydraulic head is still not even rst-order accurate. The second method gives a second-order accurate hydraulic head and at least rst-order accurate total well ux.

Second-order accurate finite volume method for well-driven flows

“…Both schemes were developed for the case of an isotropic hydraulic conductivity. An extension of these schemes to the anisotropic homogeneous case was presented in [22].…”

“…consisting of three equations of type (22) Let us assume that matrix A is invertible, and let elements of matrix A −1 be denoted by a ij . Let index k correspond to collocation points in equations of form (22) and (24) (or (27)), while indexk corresponds to Neumann boundary faces in equations of form (25). From (29), the coordinates of the unknown vector C are:…”

“…Following the same logic as in [3], it is required that α k , αk ≥ 0 for all k,k, which implies that M ± f ≥ 0, so the resulting computational matrix A(h) is an M-matrix and the method preserves the solution positivity. If this is not the case, then other equations of form (22), (24), (25), or transformed equations such as (27), are chosen to form (29).…”

Hydrodynamic simulation and analysis of groundwater regime as impacted by radial collector wells: A case study of Belgrade's water supply source

“…Za potrebe detaljne analize efekata rada BHD na hidrodinamičkim modelima, razvijen je namenski softver za simulaciju BHD i kretanja podzemnih voda pod uticajem njihovog rada. Ovaj softver (LIZZA) je prvobitno bio zasnovan na metodi konačnih elemenata, a kasnije je unapređen u metod konačnih zapremina [21,22].…”

Non-linear multi-point flux approximation in the near-well region

“…Near-well correction (NWC) scheme presented in [3,4] for non-linear two-point (TPFA) scheme is also applicable for multi-point scheme. Idea of this scheme is similar to those presented in [2], i.e.…”