气体动理学统一算法的隐式方法研究

STUDY ON IMPLICIT IMPLEMENTATION OF THE UNIFIED GAS KINETIC SCHEME

目前的气体动理学统一算法(unified gas kinetic scheme,简称UGKS)在求解高速流动问题时的计算效率,难以满足求解复杂工程问题的需求.为了提高该算法的计算效率,本文对模型方程的对流项和碰撞项进行了隐式处理,并针对UGKS界面通量与演化时间相关的特点,引入了演化时间平均界面通量,通过对控制方程矩阵进行近似LU分解(lower-upper decomposition),实现了隐式UGKS.不同来流马赫数的圆柱绕流算例测试表明,只要演化时间选取得当,隐式方法可以得到与显式方法完全相同的结果,且计算效率可以提高1～2个量级.

The current explicit unified gas kinetic scheme （UGKS） is very time-consuming for high speed flows due to the massive phase space mesh demand, which is a bottleneck for complex engineering problems. In order to improve the efficiency, the motion and collision term in the model equation is implicitly treated and the evolving time averaged flux across the cell interface is introduced, then the implicit UGKS can be obtained applying the approximate LU decompo- sition on the matrix of the governing equations. The tests on the flows over a cylinder with different freestream Mach numbers show that the implicit method can give the same result as the original explicit method with a properly chosen evolving time step, Meanwhile, the computational efficiency can be improved by 1-2 orders.