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

A high-order wall treatment is proposed and implemented into a Cartesian gr id method and the wall treatment is evaluated for incompressible turbulent flows. The Cartesian grid method employs a sequence of locally refined, uni formly spaced, Cartesian grids. In order to achieve a high-order accuracy, a wall treatment procedure has been developed for arbitrarily shaped geomet ries. The procedure consists of high-order Lagrangian polynomial interpolat ions 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 a nd a local grid refinement strategy for optimal distribution of the grid po ints. The high-order Cartesian grid method is evaluated using test function s as well as for laminar and turbulent flows. The proposed approach maintai ns the high-order discretization and yields high-order accuracy of the nume rical results. Large eddy simulation of a turbulent swirling flow indicates that the high-order wall treatment leads to significantly different result s from those calculated using a low-order piecewise constant wall descripti on. 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.