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An augmented Cartesian grid method for Stokes–Darcy fluid–structure interactions

A new finite difference method based on Cartesian meshes is proposed for solving the fluid–structure interaction between a fluid flow modeled by the Stokes equations and a porous media modeled by the Darcy's law. The idea is to introduce several augmented variables along the interface between the fluid flow and the porous media so that the problem can be decoupled as several Poisson equations. The augmented variables should be chosen so that the Beavers–Joseph–Saffman and other interface conditions are satisfied. In the discretization, the augmented variables have co‐dimension one compared with that of the primitive variables and are solved through the Schur complement system. A non‐trivial analytic solution with a circular interface is constructed to check second‐order convergency of the proposed method. Numerical examples with various interfaces and parameters are also presented. Some simulations show interesting behaviors of the fluid–structure interaction between the fluid flow and the porous media. The computational framework can be applied to other multi‐phase and multi‐physics problems. Copyright © 2015 John Wiley & Sons, Ltd.