A Mimetic Finite Volume Discretization Method for Reservoir Simulation

[1]  Stein Krogstad,et al.  Multiscale mixed/mimetic methods on corner-point grids , 2008 .

[2]  Mary F. Wheeler,et al.  A mortar mimetic finite difference method on non-matching grids , 2005, Numerische Mathematik.

[3]  Michael Andrew Christie,et al.  Tenth SPE Comparative Solution Project: a comparison of upscaling techniques , 2001 .

[4]  M. Shashkov,et al.  The mimetic finite difference method on polygonal meshes for diffusion-type problems , 2004 .

[5]  Mikhail Shashkov,et al.  Approximation of boundary conditions for mimetic finite-difference methods , 1998 .

[6]  Todd Arbogast,et al.  Logically rectangular mixed methods for Darcy flow on general geometry , 1995 .

[7]  Mary F. Wheeler,et al.  Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals , 2005, SIAM J. Numer. Anal..

[8]  Kenneth Stuart Sorbie,et al.  Permeability tensors for sedimentary structures , 1994 .

[9]  M. Shashkov,et al.  A discrete operator calculus for finite difference approximations , 2000 .

[10]  M. Shashkov,et al.  The Numerical Solution of Diffusion Problems in Strongly Heterogeneous Non-isotropic Materials , 1997 .

[11]  M. Shashkov,et al.  Natural discretizations for the divergence, gradient, and curl on logically rectangular grids☆ , 1997 .

[12]  M. Shashkov,et al.  The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes , 2006 .

[13]  M. Shashkov,et al.  A Local Support-Operators Diffusion Discretization Scheme for Hexahedral Meshes , 2001 .

[14]  Mikhail Shashkov,et al.  A tensor artificial viscosity using a mimetic finite difference algorithm , 2001 .

[15]  M. Shashkov,et al.  Mimetic Finite Difference Methods for Maxwell's Equations and the Equations of Magnetic Diffusion - Abstract , 2001 .

[16]  J. W. Watts,et al.  A Compositional Formulation of the Pressure and Saturation Equations , 1986 .

[17]  I. Aavatsmark,et al.  Control-Volume Discretization Methods for 3D Quadrilateral Grids in Inhomogeneous, Anisotropic Reservoirs , 1998 .

[18]  Knut-Andreas Lie,et al.  An Introduction to the Numerics of Flow in Porous Media using Matlab , 2007, Geometric Modelling, Numerical Simulation, and Optimization.

[19]  Konstantin Lipnikov,et al.  Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes , 2005, SIAM J. Numer. Anal..

[20]  L. Durlofsky.  Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media , 1991 .

[21]  Mikhail Shashkov,et al.  Solving Diffusion Equations with Rough Coefficients in Rough Grids , 1996 .

[22]  M.C.H. Chien,et al.  Development of a Mixed Finite-Element-Based Compositional Reservoir Simulator , 1993 .

[23]  John A. Trangenstein,et al.  Mathematical structure of compositional reservoir simulation , 1989 .

[24]  Mikhail Shashkov,et al.  The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods , 2001 .

[25]  Ruben Juanes,et al.  Implementation and Application of a Hybrid Multipoint Flux Approximation for Reservoir Simulation on Corner-Point Grids , 2005 .

[26]  Ivar Aavatsmark,et al.  Discretization on Non-Orthogonal, Quadrilateral Grids for Inhomogeneous, Anisotropic Media , 1996 .

[27]  Michael G. Edwards.  Split Full Tensor Discretization Operators for General Hexahedral Grid , 2004 .

[28]  D. Peng,et al.  A New Two-Constant Equation of State , 1976 .

[29]  Xiao-Hui Wu,et al.  Effect of Grid Deviation on Flow Solutions , 2009 .

[30]  Mikhail Shashkov,et al.  Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes , 2004 .

[31]  M. Shashkov,et al.  A new discretization methodology for diffusion problems on generalized polyhedral meshes , 2007 .

[32]  Michael G. Edwards.  Simulation With a Full-Tensor Coefficient Velocity Field Recovered From a Diagonal-Tensor Solution , 2000 .

[33]  Patrick Jenny,et al.  Implementation of a Flux-Continuous Finite-Difference Method for Stratigraphic, Hexahedron Grids , 2002 .