Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation

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Weak Galerkin method for the coupled Darcy-Stokes flow (2014, background): “Readers may refer to the nice overview [12] and references therein for its physical background, modeling, and common numerical methods.”
Analysis of the coupled Navier–Stokes/Biot problem (2017, background): “The steady-state case of this problem is analyzed mathematically in [20, 15, 2] and the time-dependent case in [13, 10, 11].”
Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems (2015, methodology): “Mathematical models and numerical algorithms for solving such coupled flow problems have been developed and analyzed during the last decade mainly for stationary single-fluid-phase systems [11, 12, 26] that describe steady-state interactions between the free flow and saturated porous media.”
Two‐phase flows in karstic geometry (2014, methodology): “Even for a small lab size conceptual model with only one conduit (pipe) imbedded in a homogenous porous media (matrix), significant mathematically rigorous progress has been achieved only recently via the so-called coupled (Navier) Stokes-Darcy model with the classical Beavers-Joseph interface bound”
Time-dependent coupling of Navier–Stokes and Darcy flows (2013, methodology): “Furthermore, it has the advantage of being independent of the Steklov-Poincaré operator used in [5,15,16] that does not seem to apply to rough interfaces.”