用格子Boltzmann模型模拟非等温流场

根据微观和宏观之间的质量、动量、能量守恒准则和在原格子Boltzmann模型基础上,建立了几个新的格子Boltzmann模型,使得在外力场中的格子Boltzmann模型得到进一步完善.通过还原宏观流体力学方程,捕捉到了浮力强迫系数与Grashof数之间的关系.所得动量方程和Navier Stokes方程相比,在黏性输运项上有明显的改进,说明黏性应力不但与流体的速度梯度和流体的压缩性有关,而且还与非定常的内能梯度和动量通量有关.该模型对非等温流场的数值结果证明了其具有很好的数值稳定性和适用性. 关键词： Boltzmann模型 平衡分布函数 流体力学方程

SIMULATION OF A FLOW FIELD WITH NONUNIFORM TEMPERATURE BY USING LATTICE BOLTZMANN EQUATION MODEL

A new lattice Boltzmann equation(LBE) model is developed based on the previous LBE model and the conservative criteria of mass, momentum and energy. The result shows that the LBE model is further improved in an external force field. The relation between the buoyancy strength parameter and the Grashof number is obtained through the recovery of dynamic equations. The viscosity transport term is obviously improved by comparing the derived momentum equation with Navier-Stokes equation. It is shown that the viscosity stress not only depends on the velocity gradient and the compressibility of the fluid, but also depends on the gradient of unsteady internal energy and unsteady momentum flux. The flow field with nonuniform temperature has been simulated by using the model. It is shown that the model is valid both in theory and in numerical experiment.