A Scheme Using the Wave Structure of Second-Moment Turbulent Models for Incompressible Flows

Martin Ferrand (1, 2) , Jean-Marc Hérard (3, 4, 1) , Thomas Norddine (3) , Simon Ruget (5)

1 CEREA - Centre d'Enseignement et de Recherche en Environnement Atmosphérique
2 EDF Labs
3 EDF - EDF
4 I2M - Institut de Mathématiques de Marseille
5 ENPC - École des Ponts ParisTech

We focus herein on the analysis of the one-dimensional Riemann problem arising from the convective subset of a second-moment turbulent non-conservative model for incompressible flows. The sketch of proof of existence and uniqueness of the solution is given, assuming a set of approximate jump conditions. Some first numerical simulations applying for the Finite Volume method are given and compared with another scheme classically used in CFD codes. This suggests to implement standard projection schemes to cope with the complete model.

Mots clés: second-moment turbulent closure incompressible turbulent flows hyperbolic systems Riemann problem; second-moment turbulent closure; incompressible turbulent flows; hyperbolic systems; Riemann problem

Domaines: Mathématiques [math]; Sciences de l'ingénieur [physics]

Martin Ferrand, Jean-Marc Hérard, Thomas Norddine, Simon Ruget. A Scheme Using the Wave Structure of Second-Moment Turbulent Models for Incompressible Flows. Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, 433, Springer Nature Switzerland, pp.111-119, 2023, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-031-40860-1_12⟩. ⟨hal-04516669⟩