An implicit high order cell-centered finite volume scheme for the solution of three-dimensional Navier-Stokes equations on unstructured grids
D. Vignerona,b,*, J.-M. Vaassena, J.-A. Essersa
aAerodynamics Group bTurbomachinery Group Département AéroSpatial Mécanique et Matériaux (ASMA), Université de Liège, Institut de Mécanique et Génie Civil (Bât. B52/3), 1, Chemin des Chevreuils, B-4000 Liège, Belgium
ABSTRACT
This paper presents a finite volume solver for the computation of three-dimensional viscous flows. A cell-centered approach is used and a quadratic reconstruction of the unknowns is performed to compute the advective fluxes on the cell faces. The gradients of the variables, necessary for the viscous fluxes, are constructed using Coirier's diamond path. A extended version of this method is proposed in this paper to ensure the consistency of the method whatever the distortion of the grid. A fully implicit time integration procedure is employed with preconditioned matrix-free GMRES solver.
Keywords:
Various flow regimes; Viscous flows; Finite volume solver; Quadratic reconstruction; Consistent viscous scheme; Newton-Krylov; Unstructured meshes