The face-centered finite volume method (FCFV) for steady-state incompressible Navier-Stokes equations

Abstract

The face-centered finite volumes (FCFV) has been proposed [2,4]. FCFV may be derived as a hybridizable discontinuous Galerkin (HDG) method with constant degree of approximation for all the variables [1,3,5]. Contrary to CCFV and VCFV approaches, the proposed FCFV method provides LBB-stable discretizations and achieves first-order convergence of velocity, pressure and gradient of velocity using unstructured meshes, without the need to perform flux reconstruction. Numerical experiments show that the method is robust in presence of distorted and stretched elements [2,4].