中文摘要：

离散速度方向模型是一种简化Boltzmann方程的新方法。该方法通过减少Boltzmann方程的维数来降低数值求解的计算量。在DVD模型中，分子速度的方向是离散的，而分子的速率仍然是连续的，这样就可以用一组三维的速率分布函数来代替Boltzmann方程中六维的速度分布函数。由于减少了三个动量维，同Boltzmann方程相比，DVD模型的数值计算量可以降低几个数量级。本文用数值的方法对DVD模型进行了研究。数值结果显示，在广泛的Knudsen数下，DVD方法可给出精确的计算结果。同线性化Boltzmann方程的计算结果相比，最大的误差不超过6％，在连续介质领域中，误差甚至不超过1％。

英文摘要：

The discrete velocity direction model is a new method to reduce the Boltzmann equation. This model reduces the computational cost of Boltzmann equation greatly by reducing three dimensions. In the model, the directions of molecules are discrete, while the molecular speed is still continuous. By this approximation, the molecular velocity distribution function in the six-dimensional phase space can be replaced by a set of speed distribution functions in the three-dimensional space. By reducing three momentum dimensions, the computational cost of Boltzmann equation can be reduced by several orders of magnitude. In this paper, the DVD model is investigated by numerical method. These results show that the DVD model is accurate in a wide range of Knudsen number. Comparing with the results by the Linearized Boltzmann equation, the largest error is less than 6%. In the continuum regime, the error is even less than 1%.