中文摘要：

提出一种基于D2Q9标准格子的低马赫数可压缩格子Boltzmann模型，模拟了管内一维气体谐振。气体振荡由位于谐振管左端的活塞振动引起，传播至右端并反射回来。利用本文模型捕捉到了谐振频率附近不同频率下的激波现象，得到了谐振频率下不同位置处轴向速度、密度和温度随时间和沿轴向的变化规律。模拟结果和理论分析及前人文献结果相一致，验证了本文所提出的基于标准格子的低马赫数可压缩格子Boltzmann模型的有效性。

英文摘要：

A double-distribution function lattice Boltzmann model is construct for low Mach number compressible flow based on standard lattice, and numerical studies are performed for gas resonant oscillations in a one-dimensional closed tube. The oscillating flow of the gas is generated by a piston at one end, and reflected by the other closed end. Shock waves with resonant frequency or slightly off-resonant frequencies are numerically captured. The time dependent velocity and density at various locations of the tube are presented. The predicted results are qualitatively consistent with those in the previous simulations, which demonstrate the validity of the presented model.