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In this work, a new discretization approach for coupled free andporous-medium flows is introduced, which uses a finite volume staggered-gridmethod for the discretization of the Navier-Stokes equations in the free-flowsubdomain, while a vertex-centered finite volume method is used in theporous-medium flow domain. The latter allows for the use of unstructured gridsin the porous-medium subdomain, and the presented method is capable of handlingnon-matching grids at the interface. In addition, the accurate evaluation ofcoupling terms and of additional nonlinear velocity-dependent terms in theporous medium is ensured by the use of basis functions and by having degrees offreedom naturally located at the interface. The available advantages of thiscoupling method are investigated in a series of tests: a convergence test forvarious grid types, an evaluation of the implementation of coupling conditions,and an example using the velocity dependent Forchheimer term in theporous-medium subdomain.

Coupling staggered-grid and vertex-centered finite-volume methods for coupled porous-medium free-flow problems