Unstructured-Grid Finite-Volume Discretization of the Navier-Stokes Equations Based on High-Resolution Difference Schemes

An unstructured-grid discretization of the Navier-Stokes equations based on the finite volume method and high-resolution difference schemes in time and space is described as applied to fluid dynamics problems in two and three dimensions. The control volume is defined as the cell-vertex median dual control volume. The fluxes through the faces of internal and boundary control volumes are written identically, which simplifies their software implementation. The gradient and the pseudo-Laplacian are calculated at the midpoint of a control volume face by using relations adapted to the computations on a strongly stretched grid in the boundary layer.