High-order Cartesian grid method for calculation of incompressible turbulent flows

A high-order wall treatment is proposed and implemented into a Cartesian grid method and the wall treatment is evaluated for incompressible turbulent flows. The Cartesian grid method employs a sequence of locally refined, uniformly spaced, Cartesian grids. In order to achieve a high-order accuracy, a wall treatment procedure has been developed for arbitrarily shaped geometries. The procedure consists of high-order Lagrangian polynomial interpolations and extrapolations for determining the dependent variables around the wall boundaries. The wall treatment procedure and the Cartesian grid method are used together with a highly efficient multi-grid acceleration method and a local grid refinement strategy for optimal distribution of the grid points. The high-order Cartesian grid method is evaluated using test functions as well as for laminar and turbulent flows. The proposed approach maintains the high-order discretization and yields high-order accuracy of the numerical results. Large eddy simulation of a turbulent swirling flow indicates that the high-order wall treatment leads to significantly different results from those calculated using a low-order piecewise constant wall description. The differences in the results are smaller at a low level of turbulence near the inlet region, but become significant in the region far away from the inlet where the turbulence is more intense. In the latter situation the effect of the wall treatment is as important as the choice of the subgrid scale stress model. Copyright (C) 2001 John Wiley & Sons, Ltd.