一种简单的局部离散速度统一气体动理论格式

统一气体动理论格式UGKS(Unified Gas-Kinetic Scheme)是一种适用于从连续流到自由分子流的全流域计算格式。在该格式中一般使用统一的离散速度空间。而在高速流动中,不同节点的分布函数往往差异很大。为了保证计算的精度,离散速度空间必须满足所有节点的需要,占用了大量的内存。采用局部的均匀离散速度空间,离散速度的范围随节点状态的变化而变化,从而降低了内存的需要,并通过引入背景网格避免了不同节点离散速度的插值。最后,通过两个一维算例对该方法进行了测试。测试结果显示,采用局部离散速度空间能够得到可靠的结果,并且在模拟高速流动时计算效率明显提高。

A simple local discrete velocity unified gas-kinetic scheme

Unified gas-kinetic scheme (UGKS) is a numerical solver in all flow regimes from continuum flow to free molecule flow.In this approach,a global discrete velocity grid is usually used.For high speed flows,the difference of distribution functions at different fluid nodes might be very large.To ensure accuracy,the discrete velocity grid must be large enough to accommodate all fluid nodes and thus a large memory storage is required.In this paper,the local uniform discrete velocity grids are used.The width of each local discrete velocity grid is determined by the local state at fluid nodes.So the requirement of memory is reduced.Through the introduction of background grid,the interpolation of discrete velocity at different nodes is avoided.The method is tested by two 1D cases.It is shown that reliable results can be obtained using a local discrete velocity grid and the computational efficiency is obviously improved in high speed cases.