过渡领域气体流动中的离散速度方向模型应用

The Application of Discrete Velocity Direction Model in Gas Flows in Transition Regime

本文发展了求解过渡领域气体流动的离散速度方向模型。在该模型中,我们用概率上的碰撞分子动量守恒来代替确定的碰撞分子动量守恒,即规定任意时刻产生相反动量变化的二体碰撞概率严格相等。新的碰撞算子可以采用任意离散速度方向和连续的速率分布函数对速度空间进行离散,从而拓展了离散速度方向方法的使用范围。为了验证新的碰撞算子在计算精度上的优越性,本文计算了Kn>1下的平板Couette流动,并与原离散速度方向模型以及线性化Boltzmann方程的相应结果进行比较。结果表明,相比原离散速度方向模型,新模型无论是剪切力还是流动速度分布的计算精度都显著提升。通过进一步验证发现,增加离散速度方向可以有效提高Kn>1下的计算精度。方腔流动的计算结果也得到了相同结论。

In this paper,we developed the Discrete Velocity Direction（DVD） model for gas flows in transition regime.The momentum conservation in a specific binary collision was replaced by the statistical momentum conservation of a group of binary collisions：we restrict that in any time interval,the possibility of binary collisions in which a momentum change would happen,is equal to the possibility of their counterpart in which the inversed momentum change happens.Under this restriction,the new collision operator could employ arbitrary velocities to discretize the velocity space in the Boltzmann Equation（BE）.The application of DVD model is broadened.To examine this new collision operator,we calculated plane Couette flows（Kn 1）.The results were compared to the same results of original DVD model and Linearized Boltzmaim Equation（LBE）.It shows that the accuracy of shearing stress and velocity profile results are both improved compared with the results of previous DVD model.Further calculation indicates that increase of the number of discrete velocity directions could improve the accuracy of simulation of Couette flows（Kn 1）.The simulation of cavity flow verifies this trend.