An IMPES scheme for a two-phase flow in heterogeneous porous media using a structured grid
Abstract
We develop a numerical scheme for a two-phase immiscible flow in heterogeneous porous media using a structured grid finite element method, which have been successfully used for the computation of various physical applications involving elliptic equations li2003new, li2004immersed, chang2011discontinuous, chou2010optimal, kwak2010analysis. The proposed method is based on the implicit pressure-explicit saturation procedure. To solve the pressure equation, we use an IFEM based on the Rannacher-Turek rannacher1992simple nonconforming space, which is a modification of the work in kwak2010analysis where `broken' P1 nonconforming element of Crouzeix-Raviart crouzeix1973conforming was developed. For the Darcy velocity, we apply the mixed finite volume method studied in chou2003mixed, kwak2010analysis on the basis of immersed finite element method (IFEM). In this way, the Darcy velocity of the flow can be computed cheaply (locally) after we solve the pressure equation. The computed Darcy velocity is used to solve the saturation equation explicitly. Thus the whole procedure can be implemented in an efficient way using a structured grid which is independent of the underlying heterogeneous porous media. Numerical results show that our method exhibits optimal order convergence rates for the pressure and velocity variables, and suboptimal rate for saturation.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.