非均匀网格湍流大涡模拟高精度有限体积解法

High accurate finite volume method on non-uniform meshes for large eddy simulation of turbulent flows

为准确预测不可压复杂湍流,提出了一种可用于大涡模拟均匀或非均匀网格上的高精度有限体积法。该方法空间离散采用有限体四阶紧致格式,时间推进采用四阶Runge-Kutta法,压力-速度耦合应用四阶紧致格式的动量插值。通过直接求解顶盖驱动方腔流动证实了该方法具有近四阶的空间精度;并在此基础上,采用动态Smagor-insky亚格子应力模式,成功地实现了充分发展槽道湍流和后台阶湍流流动的大涡模拟计算,所得结果与直接数值模拟结果吻合良好,且采用非均匀网格可在比均匀网格数少的离散系统上得到同样满意的结果。结果表明,该方法是实现高精度湍流大涡数值模拟的一个有效途径。

A high accurate finite volume method on non-uniform meshes for Large Eddy Simulation （LES） is presented in order to precisely predict complex incompressible turbulent flows. The filtered Navier-Stokes equation is solved numerically on non-staggered grids, with a finite volume fourth-order-accurate compact scheme for spatial discretization and fourthorder Runge-Kutta integration for time advancement. The pressure-velocity coupling is handled by the momentum interpolation method with a fourth-order-accurate compact scheme. In this paper the lid-driven cavity flow is calculated by direct numerical simulation （DNS） and it is evaluated that the proposed method is of fourth-order accuracy approximately. Based on the accuracy evaluation, the numerical simulations of a turbulent channel flow and a turbulent flow over a backward facing step are performed successfully by LES with a dynamic Smagroinsky model for subgfid stress. The results are in good agreement with DNS data and indicate that almost same accuracy is obtained in coarse non-uniform girds and finer uniform grids. It is concluded that the method is a powerful approach to accurately simulate the complex turbulent flows.