Stokes–Darcy coupling in severe regimes using multiscale stabilisation for mixed finite elements: monolithic approach versus decoupled approach
Keywords:
infusion, Stokes–Darcy coupled problem, monolithic approach, decoupled approach, ASGS, P1 /P1Abstract
The article exposes robust finite element solutions for coupling flows in both purely fluid region, ruled by Stokes equations, and a porous region of low permeability (down to 10−15 m2) governed by Darcy’s equations. Relying on stabilised FE formulations, two different numerical strategies are investigated for coupling Stokes–Darcy flows: a decoupled strategy, based on the use of two matching meshes and two finite element spaces for discretising the Stokes–Darcy coupled system; a unified or monolithic strategy, consisting in defining one single mesh for discretising the computational domain, associated with one single finite element space. In the first case, P1+/P1 mixed finite element is used for both Stokes and Darcy (primal form), while P1/P1 approximation is used in the second case with the dual form of the Stokes–Darcy coupled problem stabilised by a variational multi-scale method. The method of manufactured solution is used to evaluate the convergence rates of the solutions and the code robustness. Then, cases of flows normal and tangential to the Stokes–Darcy interface are investigated, and a comparison with available analytical solutions is carried out. Capabilities of both approaches are then demonstrated in solving problems with complex geometry and 3D cases.
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