Decoupled Algorithms for the Coupled Surface /Subsurface Flow Interaction Problems

Abstract

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.