Proper Finite Difference Schemes for Simulations of Incompressible Turbulent Flow in Generalized Curvilinear Coordinates : (2nd Report, Validation of finite difference schemes in Generalized Curvilinear Coordinates)

Abstract

In this second report, the conservation properties of finite difference schemes in generalized curvilinear coordinate system constructed in the first report are examined by numerical tests of two-dimensional inviscid flow with periodic domains. It is confirmed that the modified finite difference scheme in a colocated grid layout conserves the mass and kinetic energy properly even in nonorthogonal nonuniform computational grid. The conservation properties of the finite difference scheme in a staggered grid layout are also proper only when computational grids are orthogonal. In addition, direct numerical simulations of a plane channel flow with fairly coarse mesh at Re_τ-180 are conducted using the finite difference schemes in generalized curvilinear coordinate system. It is found that the mesh dependency such as nonorthogonality and nonuniformity on results is reduced by the modified finite difference schemes in the colocated grid layout.