Compatible Discrete Operator schemes for the steady incompressible Stokes and Navier-Stokes equations

Riccardo Milani (1, 2, 3) , Jérôme Bonelle (3) , Alexandre Ern (2, 1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms
3 EDF R&D MFEE - Mécanique des Fluides, Energies et Environnement

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 sub-cell 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.

Mots clés: CDO; Stokes; Navier-Stokes; Structure-preserving schemes

Domaines: Equations aux dérivées partielles [math.AP]; Modélisation et simulation; Mécanique des fluides [physics.class-ph]

Riccardo Milani, Jérôme Bonelle, Alexandre Ern. Compatible Discrete Operator schemes for the steady incompressible Stokes and Navier-Stokes equations. FVCA - Finite Volumes for Complex Applications IX, Jun 2020, Bergen, Norway. ⟨hal-02417514v2⟩