A discontinuous Galerkin method for two-phase flow in a porous medium enforcing H(div) velocityand continuous capillary pressure

被引：38

作者：

Arbogast, Todd ^{[1
]}

Juntunen, Mika ^{[2
]}

Pool, Jamie ^{[1
]}

Wheeler, Mary F. ^{[1
]}

机构：

[1] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA

[2] Aalto Univ, Sch Sci, Dept Math & Syst Anal, FI-00076 Aalto, Finland

来源：

COMPUTATIONAL GEOSCIENCES | 2013年 / 17卷 / 06期

关键词：

Finite element method; FEM; Discontinuous Galerkin; DG; Flow in porous media; Capillary pressure; IMPES; RECONSTRUCTION; APPROXIMATIONS;

D O I：

10.1007/s10596-013-9374-y

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We consider the slightly compressible two-phase flow problem in a porous medium with capillary pressure. The problem is solved using the implicit pressure, explicit saturation (IMPES) method, and the convergence is accelerated with iterative coupling of the equations. We use discontinuous Galerkin to discretize both the pressure and saturation equations. We apply two improvements, which are projecting the flux to the mass conservative H(div)-space and penalizing the jump in capillary pressure in the saturation equation. We also discuss the need and use of slope limiters and the choice of primary variables in discretization. The methods are verified with two- and three-dimensional numerical examples. The results show that the modifications stabilize the method and improve the solution.

引用

页码：1055 / 1078

页数：24

共 17 条

[1]

[Anonymous], 2006, Comput. Sci. Eng.

[2]

[Anonymous], 1977, Fundamentals of numericl reservoir simulation

[3] A multiscale mortar mixed finite element method [J].

Arbogast, Todd ;

Pencheva, Gergina ;

Wheeler, Mary F. ;

Yotov, Ivan .

MULTISCALE MODELING & SIMULATION, 2007, 6 (01) :319-346

[4] Superconvergence and H(div) projection for discontinuous Galerkin methods [J].

Bastian, P ;

Rivière, B .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2003, 42 (10) :1043-1057

[5]

Bear J., 2010, MODELING GROUNDWATER

[6]

Brezzi F., 1991, Mixed and Hybrid Finite Element Methods, DOI [10. 1007/978-1-4612- 3172-1., DOI 10.1007/978-1-4612-3172-1]

[7] A benchmark study on problems related to CO2 storage in geologic formations [J].

Class, Holger ;

Ebigbo, Anozie ;

Helmig, Rainer ;

Dahle, Helge K. ;

Nordbotten, Jan M. ;

Celia, Michael A. ;

Audigane, Pascal ;

Darcis, Melanie ;

Ennis-King, Jonathan ;

Fan, Yaqing ;

Flemisch, Bernd ;

Gasda, Sarah E. ;

Jin, Min ;

Krug, Stefanie ;

Labregere, Diane ;

Beni, Ali Naderi ;

Pawar, Rajesh J. ;

Sbai, Adil ;

Thomas, Sunil G. ;

Trenty, Laurent ;

Wei, Lingli .

COMPUTATIONAL GEOSCIENCES, 2009, 13 (04) :409-434

[8] Compatible algorithms for coupled flow and transport [J].

Dawson, C ;

Sun, SY ;

Wheeler, MF .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2004, 193 (23-26) :2565-2580

[9] Fully implicit discontinuous finite element methods for two-phase flow [J].

Epshteyn, Y. ;

Riviere, B. .

APPLIED NUMERICAL MATHEMATICS, 2007, 57 (04) :383-401

[10] Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures [J].

Ern, A. ;

Mozolevski, I. ;

Schuh, L. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (23-24) :1491-1501

← 1 2 →