Investigating a High-Order Viscous Flux Scheme for Unstructured Grids

A viscous flux formulation at interior faces and at Dirichlet boundary conditions in the framework of unstructured vertex-centered [Formula: see text]-exact finite-volume schemes is presented. It is based on a geometric decomposition of the viscous flux into orthogonal and nonorthogonal parts. Special emphasis is put on the truncation errors and the spectral properties of the scheme, and a connection is established to the well-known [Formula: see text]-damping scheme. The latter is also used to introduce discretization coefficients into the method that allow a fourth and a sixth order of accuracy in space on Cartesian grids. The effect of the scheme is presented in terms of canonical diffusion problems, as well as test cases for laminar wall-bounded flows. It is shown that the method preserves a second-order accuracy for the viscous operator, even on highly distorted unstructured grids and in the presence of boundaries and that it strongly enhances the solution accuracy with respect to a conventional scheme for viscous fluxes.