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

Abstract

SUMMARYA 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.

Large eddy simulations of turbulent swirling flows in a dump combustor: a sensitivity study

“…In a low-order wall boundary treatment, a curve wall is represented by piecewise step-walls. Gullbrand et al [19] developed a high-order wall algorithm, in which the uniform grid is kept at the wall, with the wall boundary condition being fulÿlled at the exact wall location by using an interpolation and extrapolation procedure of the dependent variables.…”

“…The basic idea is to use the Cartesian grid for obtaining a high-order numerical discretization of the governing PDE, and to minimize the ÿlter=ÿnite di erence commutation errors. In order to overcome the shortcoming of Cartesian grid in dealing with curve wall boundaries, a high-order accuracy wall algorithm [19] is used.…”

“…This set of governing equations is appropriate for low Mach number ows. The numerical simulations are based on a so-called Cartesian grid method developed previously [19]. The basic idea is to use the Cartesian grid for obtaining a high-order numerical discretization of the governing PDE, and to minimize the ÿlter=ÿnite di erence commutation errors.…”

Assessment of volume of fluid and immersed boundary methods for droplet computations

“…The accuracy of the spatial discretizations of the momentum equations is improved to third order for convective terms and fourth order for other terms by a single-step defect correction [12,13]. The reason for using defect correction instead of a pure high order scheme is related to the enhanced stability properties of the low order algorithm combined with the accuracy of the high order operator.…”

Effects of aerodynamic particle interaction in turbulent non-dilute particle-laden flow

“…This approach has an increasing acceptance as due to increase in computational resources a larger part of the turbulence spectrum can be resolved and the unresolved kinetic energy therefore declines with increasing resolution. In this respect, LES is an approximation to DNS, and therefore it is conceptually acceptable that no explicit SGS model is required [34][35][36]. SGS models should drain energy at the smallest resolved waves but should be negligible for the largest waves.…”