An adaptive multigrid upwind solver for compressible viscous flows

This paper provides an accurate and efficient methodology for solving the two- and threedimensional Navier-Stokes equations. A flux difference splitting method with a formally second-orderaccurate upwind space discretization is employed for the inviscid fluxes, whereas a central scheme is used for the diffusive ones. Efficiency is enhanced by means of a local time stepping and a full multigrid technique with an explicit time integration scheme. Furthermore, a solution-adaptive local gridrefinement strategy is combined with the multigrid cycle. The methodology is applied to the computation of the two-dimensional laminar and turbulent viscous flows about an isolated airfoil and through two different cascades, whereas the turbulent flow inside the Stanitz elbow is considered as a threedimensional test case. The main aspects concerning accuracy and efficiency are discussed by comparing the computed results with numerical and experimental data available in the literature