Kinetic energy control in explicit Finite Volume discretizations of the incompressible and compressible Navier-Stokes equations

T Gallouët (1) , R Herbin (1) , J.-C Latché (2)

1 I2M - Institut de Mathématiques de Marseille
2 IRSN - Institut de Radioprotection et de Sûreté Nucléaire

We prove that, under a cfl condition, the explicit upwind finite vol-ume discretization of the convection operator C(u) = ∂ t (ρu) + div(uq), with a given density ρ and momentum q, satisfies a discrete kinetic energy decrease property, provided that the convection operator satis-fies a "consistency-with-the-mass-balance property", which can be simply stated by saying that it vanishes for a constant advected field u.

Mots clés: Compressible Navier-Stokes equations; Finite Volume dis-cretizations; Stability; Kinetic Energy

Domaines: Analyse numérique [math.NA]

T Gallouët, R Herbin, J.-C Latché. Kinetic energy control in explicit Finite Volume discretizations of the incompressible and compressible Navier-Stokes equations. International Journal on Finite Volumes, 2010, 7 (2), pp.1-6. ⟨hal-01112391⟩