A finite volume method with conservative and consistent viscous terms discretization for three-dimensional flows

A finite volume solver is presented in this paper and is designed for the computation of
three-dimensional viscous flows on unstructured meshes. A cell-centered approach is used
and the advective fluxes on the cell faces are computed by upwind methods combined with a
quadratic reconstruction of the unknowns on these faces. The diffusive terms are computed
by the finite volume approach, ensuring conservativity, and the required gradients of the
variables on the faces 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.