从离散速度模型到矩方法

FROM DISCRETE VELOCITY MODEL TO MOMENT METHOD

为了求解动理学方程,我们通过研究一维情形下的离散速度模型,发现通过对离散速度点使用自适应技术可以直接得到Grad矩方程组.作为一个统一的认识,矩方程组可以看作是对离散速度点自适应的离散速度模型,而离散速度模型可以看作是取特别形式的"矩"的矩方程组.这使得我们可以在一致的框架下来理解离散速度模型和矩方法,而不是将它们对立起来.为了建立这样的一致框架,最近在[2]中发展的正则化理论是根本性的.

In numerical approaches for the Boltzmann equation, the discrete velocity model and the moment method are formally very different. In this paper, we try to show the intrinsic connection between these two approaches. Precisely, the Grad type moment method with appropriate closure can be regarded as a discrete velocity model with some adaptivities in setup of the velocity points. The globally hyperbolic regulazation of the moment method plays an essential role in connecting both aDDroaches toe＇etber.