2023/03/20 by E Chénier, Chénier, E, Erell Jamelot +5
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2303.10918
openalex publication_date 2023/03/20 · openalex created_date 2023/03/23 · openalex updated_date 2026/07/28
The resolution of the incompressible Navier-Stokes equations is tricky, and it is well known that one of the major issue is to compute a divergence free velocity. The non-conforming Crouzeix-Raviart finite element are convenient since they induce local mass conservation. Moreover they are such that the stability constant of the Fortin operator is equal to 1. This implies that they can easily handle anisotropic mesh [1, 2]. However spurious velocities may appear and damage the approximation. We propose a scheme here that allows to reduce the spurious velocities. It is based on a new discretisation for the gradient of pressure based on the symmetric MPFA scheme (finite volume MultiPoint Flux Approximation) [3, 4, 5].