Numerical solution to a mixed Navier-Stokes/Darcy model by the two-grid approach. (English) Zbl 1213.76131

Cai, Mingchao; Mu, Mo; Xu, Jinchao

SIAM J. Numer. Anal. 47, No. 5, 3325-3338 (2009).

The authors study numerical methods for a coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through a porous medium. A mathematical model and its properties for the coupled fluid flow and porous medium equations are described. Since the numerical difficulties increase as the mesh size decreases, the authors propose an alternative decoupled and linearized two-grid algorithm. In the decoupled algorithm, one solves the coupled nonlinear problem on a coarse grid, and two decoupled and linear local problems on a fine grid. The two-grid algorithm is numerically efficient because it enables the application of the most efficient and optimized local linear solvers, and it allows for easy and efficient implementation and software reuse by plugging in the existing local solvers. The authors also show that the two-grid algorithm, with a properly chosen coarse grid, still retains the same order of accuracy as the coupled nonlinear algorithm.

Reviewer: Adrian Carabineanu (Bucureşti)

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
76D05	Navier-Stokes equations for incompressible viscous fluids
76S05	Flows in porous media; filtration; seepage
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs

Keywords:

interface coupling; decoupling; linearization