四阶紧致格式有限体积法湍流大涡模拟

Fourth-order compact scheme finite volume method for large eddy simulations of turbulent flows

为准确预测不可压复杂湍流,提出了一种应用于大涡模拟的高精度有限体积法。该方法在非交错网格上数值求解大涡模拟方程,空间离散采用有限体四阶紧致格式,时间推进用四阶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和振荡平板上方的流动,证实了该方法具有近四阶精度;并在此基础上,采用动力Smagorinsky亚格子应力模式,成功地完成了充分发展槽道湍流的大涡模拟计算,所得结果与直接数值模拟结果吻合良好。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。

An high accurate finite volume method for large eddy simulations （LES） was developed to precisely predict complexs incompressible turbulent flows. The filtered Navier-Stokes equations were solved numerically on non-staggered grids, with a fourth-order-accurate compact finite volume scheme for spatial discretization and a fourth-order Runge-Kutta integration for the time step. The pressure-velocity coupling was handled using the momentum interpolation method with a fourth-order-accurate compact scheme. Analysis of the lid-driven cavity flow problem and flow over an oscillating plate shows that the method is approximately fourth-order accurate. Turbulent channel flow was then analyzed with the dynamic Smagroinsky model for the subgrid stresses. The results agree well with direct numerical simulation （DNS） results which shows that the method can be used to accurately simulate complex turbulent flows.