A discrete kinetic energy preserving convection operator for variable density flows on locally refined staggered meshes

J.-C Latché (1) , B Piar (1) , Khaled Saleh (2, 3, 4)

1 IRSN - Institut de Radioprotection et de Sûreté Nucléaire
2 ICJ - Institut Camille Jordan
3 UCBL - Université Claude Bernard Lyon 1
4 MMCS - Modélisation mathématique, calcul scientifique

In this paper, we build and analyze a scheme for the time-dependent variable density Navier-Stokes equations, able to cope with unstructured non-conforming meshes, with hanging nodes. The time advancement relies on a pressure correction algorithm and the space approximation is based on a low-order staggered non-conforming finite element, the so-called Rannacher-Turek element. The convection term in the momentum balance equation is discretized by a finite volume technique, and a careful construction of the fluxes, especially through non-conforming faces, ensures that the solution obeys a discrete kinetic energy balance. Its consistency is addressed by analyzing a model problem, namely the convection-diffusion equation, for which we theoretically establish a first order convergence in space for energy norms. This convergence order is also observed in the numerical experiments for the Navier-Stokes equations. Navier-Stokes equations, pressure correction scheme, finite volumes, finite elements, stability, kinetic energy, non-conforming local refinement.

Domaines: Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

J.-C Latché, B Piar, Khaled Saleh. A discrete kinetic energy preserving convection operator for variable density flows on locally refined staggered meshes. 2019. ⟨hal-02391939⟩