Numerical Solution to a Mixed Navier-Stokes/Darcy Model by the Two-Grid Approach

We study numerical methods for a coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. A decoupled and linearized two-grid algorithm is proposed. Numerical analysis and experiments are presented to show the efficiency and effectiveness of the decoupled and linearized algorithm.

[1]  William Layton,et al.  Two-level Picard and modified Picard methods for the Navier-Stokes equations , 1995 .

[2]  Ivan Yotov,et al.  Coupling Fluid Flow with Porous Media Flow , 2002, SIAM J. Numer. Anal..

[3]  Howard C. Elman,et al.  Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics , 2014 .

[4]  A. Bejan,et al.  Convection in Porous Media , 1992 .

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

[6]  VIVETTE GIRAULT,et al.  DG Approximation of Coupled Navier-Stokes and Darcy Equations by Beaver-Joseph-Saffman Interface Condition , 2009, SIAM J. Numer. Anal..

[7]  Willi Jäger,et al.  On The Interface Boundary Condition of Beavers, Joseph, and Saffman , 2000, SIAM J. Appl. Math..

[8]  F. Brezzi,et al.  Finite dimensional approximation of nonlinear problems , 1981 .

[9]  Marco Discacciati,et al.  Domain decomposition methods for the coupling of surface and groundwater flows , 2004 .

[10]  William Layton,et al.  A two-level discretization method for the Navier-Stokes equations , 1993 .

[11]  A. Quarteroni,et al.  Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations , 2004 .

[12]  Mingchao Cai Modeling and numerical simulation for the coupling of surface flow with subsurface flow , 2008 .

[13]  Jinchao Xu Two-grid Discretization Techniques for Linear and Nonlinear PDEs , 1996 .

[14]  Alfio Quarteroni,et al.  Domain Decomposition Methods for Partial Differential Equations , 1999 .

[15]  Jacques Rappaz,et al.  Finite Dimensional Approximation of Non-Linear Problems .1. Branches of Nonsingular Solutions , 1980 .

[16]  V. Girault,et al.  Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra. , 2001 .

[17]  Jinchao Xu,et al.  A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow , 2007, SIAM J. Numer. Anal..

[18]  R. Temam Navier-Stokes Equations , 1977 .

[19]  D. Joseph,et al.  Boundary conditions at a naturally permeable wall , 1967, Journal of Fluid Mechanics.

[20]  Vivette Girault,et al.  Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[21]  O. Karakashian On a Galerkin--Lagrange Multiplier Method for the Stationary Navier--Stokes Equations , 1982 .

[22]  E. Miglio,et al.  Mathematical and numerical models for coupling surface and groundwater flows , 2002 .

[23]  B. Rivière,et al.  On the solution of the coupled Navier–Stokes and Darcy equations , 2009 .

[24]  P. Saffman On the Boundary Condition at the Surface of a Porous Medium , 1971 .