点隐式龙格-库塔方法的应用研究

Some Investigations on Applications of Point-implicit Runge-Kutta Method

为了提高求解器的效率,在显式龙格-库塔时间推进的欧拉方程求解器之上,发展了点隐式龙格-库塔时间推进格式。给出了其推导过程和非结构网格下中心格式和迎风格式(Roe和Van Leer格式)预处理算子的构造方法。NACA0012翼型和RAE2822翼型的跨音速无粘流动模拟表明:与显式龙格-库塔方法相比,方法能提高求解效率且内存需求相当,具有一定的工程应用价值。

In order to improve the efficiency of flow solver,a point-implicit Runge-Kutta method is raised on the basis of the Euler solver with an explicit Runge-Kutta method time marching.The derivation of preconditioner is presented.Its constructions,according to the central and upwind（Roe-and Van Leer-scheme） spatial discretization,based on unstructured grid are given,respectively.The simulations of the transonic inviscid flow around NACA0012 and RAE2822 show that comparing with the explicit Runge-Kutta method,the efficientcy is improved by the presented algorithm with a moderate memory increment.