含激波的湍流流动高精度大涡数值模拟方法（英文）

High Order Numerical Methods for LES of Turbulent Flows with Shocks

针对采用亚格子模型进行含激波的湍流流动模拟时会面临激波附近的精度损失问题,考虑从通过亚格子模型以及数值模拟方法两方面的改进来实现湍流流动大涡模拟的精度提高。大涡模拟采用了Yee及Sjgreen(2009)提出的高阶低耗散方法。该方法采用自适应的流场探测器以控制计算中所需区域的数值耗散,并考虑对动力学模型采用在激波位置使用Sagaut和Germano(2005)提出的单边亚格子过滤器和(或)直接禁用亚格子项等方法加以改进。对于标准的马赫数1.5和3条件下的激波-湍流干扰问题,上述新方法相较于全区域采用亚格子模型的方法均表现出了相似的精度提升。同时实现的数值精度改进方案采用了Harten的亚单元分辨过程来定位和锐化激波,并在精确激波位置附近的网格点处采用了单边测试滤波。

Simulation of turbulent flows with shocks employing subgrid-scale （SGS） filtering may encounter a loss of accuracy in the vicinity of a shock.This paper addresses the accuracy improvement of LES of turbulent flows in two ways：（a） from the SGS model standpoint and （b） from the numerical method improvement standpoint.The high order low dissipative method of Yee ＆ Sj（o）green （2009） using adaptive flow sensors to control the amount of numerical dissipation where needed is used for the LES simulation.The considered improved dynamics model approaches include applying the one-sided SGS test filter of Sagaut ＆ Germano （2005） and/or disabling the SGS terms at the shock location.For Mach 1.5 and 3 canonical shock-turbulence interaction problems both of these new approaches show a similar accuracy improvement to that of the full use of the SGS terms.One of the numerical accuracy improvements included here applies Harten＇s subcellre solution procedure to locate and sharpen the shock,and uses a one-sided test filter at the grid points adjacent to the exact shock location.