A convergent FV–FE scheme for the stationary compressible Navier–Stokes equations. (19th May 2020)

• Record Type: Journal Article
• Authors: Perrin, Charlotte; Saleh, Khaled
• Is Part Of: IMA journal of numerical analysis. Volume 41:Number 2(2021)
• Page Start: 826
• Page End: 899
• Publication Date: 2020-05-19
• Subjects: Stationary compressible Navier–Stokes equations -- staggered discretization -- finite volume–finite element method -- convergence analysis; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/draa003
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: 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 $p(\rho )=a \rho ^{\gamma }$ with $\gamma> \frac{3}{2}$ . It is the first convergence result for a numerical method with adiabatic exponents $\gamma $ less than $3$ when the space dimension is 3. 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 3 S developed by the French Institut de Radioprotection et de Sûreté Nucléaire.