Discretization Methodology for High Aspect Ratio Prismatic Grids

The stability and accuracy of several discretization schemes are evaluated for high aspect ratio prismatic grids. Both inviscid and viscous discretizations are studied using the method of manufactured solutions by systematically varying parameters such as the aspect ratio, mesh stretching, curvature, skewness, and non-planar faces. For the inviscid terms, gradient reconstruction based on cell least squares and nodal Green-Gauss are considered. In particular, high curvature grids are shown to lead to instabilities with both classes of schemes and a new Green-Gauss scheme based on nodal projection is developed that retains stability and formal second-order accuracy under all conditions. A further advantage of the nodal Green-Gauss schemes is that the nodal values can be used in the viscous discretization as well. All the viscous schemes tested here are demonstrated to preserve second-order accuracy. Finally, for three-dimensional prismatic meshes, triangulation of non-planar faces is found to be necessary to preserve second-order accuracy.