A zonal finite element method and some related issues for calculating compressible and incompressible viscous flows

A viscous-inviscid zonal method is presented for simulating compressible and incompressible viscous flows. In the method, the computational domain is divided into an inviscid zone, where an inviscid solver is used, and a viscous zone near the body surface and its wake, where a Navier-Stokes solver is employed to deal with the viscous flow. The computational efficiency is thus improved by reducing the extent of the viscous computational domain. The coupling is made along a patching boundary, located in the inviscid part of the flow. A finite element method is used to deal with both the inviscid and viscous problems. The inviscid solution is computed by solving the potential flow with a density upwind (also called artificial compressibility) finite element method. The viscous solution is obtained by solving Reynolds-averaged Navier-Stokes (RANS) equations via a streamline upwind Petrov-Galerkin finite element method. Numerical results are presented for two-dimensional compressible and incompressible high Reynolds number turbulent flows around an NACA 0012 airfoil. The results by the present viscous-inviscid methods are in close agreement with the full Navier-Stokes solutions by the present author and others. (author)