DG Approximation of Coupled Navier-Stokes and Darcy Equations by Beaver-Joseph-Saffman Interface Condition

By Vivette Girault, Beatrice M. Riviere. SIAM Journal on Numerical Analysis, 2009

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Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation (2009, methodology): “DG methods based on Interior Penalty are considered in [112, 75] for both the fluid and the groundwater problem, and all unknowns are approximated by totally discontinuous polynomials of different orders.”
Navier–Stokes/Forchheimer models for filtration through porous media (2013, methodology): “Moreover, the case of the Navier-Stokes equations has been considered in 47 [3, 14, 19, 31].”
Two‐phase flows in karstic geometry (2014, methodology): “In this case, it may be useful to employ the so-called Lions interface boundary condition [13, 73, 82, 83, 84]”
Time-dependent coupling of Navier–Stokes and Darcy flows (2013, background): “in [5], by Girault and Rivière in [18], and by Chidyagwai and Rivière in [11, 12].”
Analysis of the coupled Navier–Stokes/Biot problem (2017, background): “The following inf-sup condition holds [20, 11]: There exists a constant κ > 0 such that”