High aspect ratio grid effects on the accuracy of Navier-Stokes solutions on unstructured meshes
The method of manufactured solutions is used to evaluate the stability and accuracy of several unstructured discretization schemes in the presence of high-aspect ratio grids. Both inviscid and viscous discretizations are studied 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 meshes, triangulation of non-planar faces is found to be necessary to preserve second-order accuracy. (c) 2012 Elsevier Ltd. All rights reserved.
method of manufactured solutions computational fluid dynamics mesh quality unstructured grids high aspect-ratio grids