A Zonal Finite Element Method and Some Related Issues for Calculating Compressible and Incompressible Viscous Flows

摘要

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.