A hybridizable discontinuous Galerkin method for the coupled Navier–Stokes/Biot problem

In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier–Stokes equations coupled to the quasi-static poroelasticity equations via interface conditions. We determine a bound on the data that guarantees stability and well-posedness of the fully discrete problem and prove a priori error estimates. A numerical example confirms our analysis.