A convergent FV-FE scheme for the stationary compressible Navier-Stokes equations

Charlotte Perrin (1) , Khaled Saleh (2, 3)

1 I2M - Institut de Mathématiques de Marseille
2 MMCS - Modélisation mathématique, calcul scientifique
3 UCBL - Université Claude Bernard Lyon 1

In this paper, we prove a convergence result for a discretization of the three-dimensional stationary compressible Navier-Stokes equations assuming an ideal gas pressure law p(ρ) = aρ^γ with γ > 3/2. It is the first convergence result for a numerical method with adiabatic exponents γ less than 3 when the space dimension is three. The considered numerical scheme combines finite volume techniques for the convection with the Crouzeix-Raviart finite element for the diffusion. A linearized version of the scheme is implemented in the industrial software CALIF^3S developed by the french Institut de Radioprotection et de S\^uret\'e Nucl\'eaire (IRSN).

Mots clés: staggered discretization; Stationary compressible Navier-Stokes equations; finite volume - finite element method; convergence analysis

Domaines: Analyse numérique [math.NA]

Charlotte Perrin, Khaled Saleh. A convergent FV-FE scheme for the stationary compressible Navier-Stokes equations. IMA Journal of Numerical Analysis, 2021, 41 (2), pp.826-899. ⟨10.1093/imanum/draa003⟩. ⟨hal-02175302v2⟩