Compatible discrete operator schemes for the steady incompressible stokes and navier–stokes equations

Abstract

We extend the Compatible Discrete Operator (CDO) schemes to the steady incompressible Stokes and Navier–Stokes equations. The main features of the CDO face-based schemes are recalled: a hybrid velocity discretization with degrees of freedom at faces and cells, a stabilized velocity gradient reconstruction defined on the face-based subcell pyramids, and a discrete pressure attached to the mesh cells. We introduce a discrete divergence operator that will account for the velocity-pressure coupling, and a hybrid discretization of the convection term. The results of several benchmark test cases validate the framework.