Discontinuous Galerkin methods for the Navier–Stokes equations using solenoidal approximations

Abstract

An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier–Stokes equations. Both compact formulations can be easily applied using high-order piecewise divergence-free approximations, leading to two uncoupled problems: one associated with velocity and hybrid pressure, and the other one only concerned with the computation of pressures in the elements interior. Numerical examples compare the efficiency and the accuracy of both proposed methods.