热分层湍流直接模拟的高精度算法和数值分析

Direct simulations of thermal stratified turbulent flow using high-order finite-difference schemes

该文发展了高阶精度有限差分格式的直接数值模拟方法,并将其成功地应用于带有自由面的热分层槽道湍流问题的计算,与低阶精度格式相比,高精度格式有着更宽的低耗散波段,对中高波数分量有较好的模拟能力。该文直接在非均匀网格上采用Lagrange多项式插值构造迎风偏置格式,克服了传统二阶格式在网格变化剧烈时精度损失的缺点,提高了在近壁区的计算精度。对三维槽道湍流以及带有自由面的热分层湍流的流场和温度场的统计特征、脉动特征以及能谱进行了分析,进一步验证了高精度差分方法对热分层剪切湍流问题直接模拟的有效性。总体上讲,该格式精度高,对高频非物理振荡有抑制作用,可以适应变化的空间网格,有效地模拟复杂湍流流动结构,并正确地揭示其流动机理.

Direct numerical simulation of stably and unstably stratified turbulent open channel flow was performed. Three-dimensional Navier-Stokes and energy equations under the Boussinesq approximation were numerically solved using a fi＇actional-step method based on high-order accurate spatial schemes. The approach based on the high-order accurate schemes is a good candidate for direct simulations of turbulent flows, because results calculated by the approach appear far superior to those obtained with conventional second-order schemes. To elucidate the turbulent flow and heat transfer behaviors, some typical quantities including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and the structures of velocity and temperature fluctuations were obtained and analyzed.