Miscible displacement simulation by finite element methods in distributed memory machines

Abstract Finite element methods taylored for large scale simulation of incompressible miscible displacement in porous media are presented. Employing same order Lagrangian interpolations for all variables, pressure is approximated by Galerkin's method, global or local post-processing techniques are used to compute higher-order velocity approximations, and a stabilized Petrov—Galerkin formulation is applied to concentration equation. Error estimates are discussed as well as the parallel implementation on a distributed memory machine. Numerical simulations of tracer injection processes and miscible displacements with high adverse mobility ratios in two and three dimensions are reported.

[1]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[2]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[3]  Fernando A. Rochinha,et al.  Higher-order gradient post-processings for second-order elliptic problems , 1995 .

[4]  T. F. Russell,et al.  Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics , 1984 .

[5]  L. D. Marini,et al.  Two families of mixed finite elements for second order elliptic problems , 1985 .

[6]  A. Loula,et al.  Numerical analysis of finite element methods for miscible displacements in porous media , 1998 .

[7]  Richard E. Ewing,et al.  The approximation of the pressure by a mixed method in the simulation of miscible displacement , 1983 .

[8]  William B. Zimmerman,et al.  Nonlinear viscous fingering in miscible displacement with anisotropic dispersion , 1991 .

[9]  Alvaro L. G. A. Coutinho,et al.  37399 - Parallel Finite Element Simulation of Miscible Displacements in Porous Media , 1996 .

[10]  William Gropp,et al.  Skjellum using mpi: portable parallel programming with the message-passing interface , 1994 .

[11]  Claes Johnson,et al.  Finite element methods for linear hyperbolic problems , 1984 .

[12]  Anthony Skjellum,et al.  Using MPI - portable parallel programming with the message-parsing interface , 1994 .