Research works on the coupling of incompressible surface flow with subsurface
porous media flow arouse increasing interest recently. The coupled problems are typical
multi-domain problems with multi-physics. Correspondingly, the heterogeneous partial
differential equations for modeling these problems are coupled together at the interface
between different domains. In the present work, we mainly study numerical methods for
the coupled (Navier-) Stokes/Darcy models, which are typical models for stationary surface/
subsurface flow interactions. We propose several decoupled algorithms so that numerical
computations can be realized in parallel. Specifically, we investigate decoupled preconditioning
techniques and two grid algorithms. Numerical examples and mathematical
analysis are given to show that these algorithms are effective and efficient.
Keywords: Coupled Stokes/Darcy model, decoupled algorithms, decoupled preconditioning techniques,
GMRES method, incompressible surface flow, multidomain coupled problems, multilevel algorithm, Newtonian
fluid flow, Oseen/Darcy model, Picard iteration, SaintVenant equations, shallow water equations,
subsurface porous media flow.
