Interface solvers and preconditioners of domain decomposition type for multiphase flow in multiblock porous media

A multiblock mortar approach to modeling multiphase flow in porous media decomposes the simulation domain into a series of blocks with possibly different physical and numerical models employed in each block. Matching conditions along the interfaces are imposed through the use of mortar finite elements. A parallel domain decomposition algorithm reduces the algebraic nonlinear system to an interface problem which is solved via a nonlinear multigrid with Newton-GMRES smoothing.

[1]  Jean E. Roberts,et al.  Mixed and hybrid finite element methods , 1987 .

[2]  F. Brezzi,et al.  Mathematical models and finite elements for reservoir simulation : single phase, multiphase and multicomponent flows through porous media , 1988 .

[3]  Denise Ferembach.  Vandermeersch (В.). — Les hommes fossiles de Qafzeh (Israël). Thèse de Doctorat d'Etat es Sciences. Université Pierre et Marie Curie. , 1977 .

[4]  J. Mandel,et al.  Balancing domain decomposition for mixed finite elements , 1995 .

[5]  C. Bernardi,et al.  A New Nonconforming Approach to Domain Decomposition : The Mortar Element Method , 1994 .

[6]  P. Raviart,et al.  A mixed finite element method for 2-nd order elliptic problems , 1977 .

[7]  D. Evelyne.  Thèse de doctorat d'Etat , 1988 .

[8]  Todd Arbogast,et al.  A non-mortar mixed finite element method for elliptic problems on non-matching multiblock grids☆ , 1997 .

[9]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[10]  C. Kelley.  Iterative Methods for Linear and Nonlinear Equations , 1987 .

[11]  I. Yotov,et al.  Mixed Finite Element Methods on Non-Matching Multiblock Grids , 1996 .

[12]  Todd Arbogast,et al.  Mixed Finite Element Methods on Nonmatching Multiblock Grids , 2000, SIAM J. Numer. Anal..

[13]  Mary F. Wheeler,et al.  A parallel, implicit, cell‐centered method for two‐phase flow with a preconditioned Newton–Krylov solver , 1997 .

[14]  Ivan Yotov,et al.  Mixed finite element methods for flow in porous media , 1996 .

[15]  Todd Arbogast,et al.  Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry , 1998, SIAM J. Sci. Comput..

[16]  A Mixed Nite Element Discretization on Non-matching Multiblock Grids for a Degenerate Parabolic Equation Arising in Porous Media Ow , 1997 .

[17]  M. Wheeler,et al.  Multigrid on the interface for mortar mixed finite element methods for elliptic problems , 2000 .

[18]  Faker Ben Belgacem,et al.  The Mortar finite element method with Lagrange multipliers , 1999, Numerische Mathematik.

[19]  M. Wheeler,et al.  Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite Differences , 1997 .

[20]  Malgorzata Peszynska,et al.  Multiphysics coupling of codes , 2000 .

[21]  Mary F. Wheeler,et al.  Parallel Domain Decomposition Method for Mixed Finite Elements for Elliptic Partial Differential Equations , 1990 .

[22]  G. Chavent.  Mathematical models and finite elements for reservoir simulation , 1986 .