中文摘要：

将无网格自适应算法发展用于求解存在运动激波的非定常流动问题。为了降低初始布点要求,同时提高对运动激波的分辨率,提出了一种结合点云加密和点云粗化的动态点云技术。采用该技术,在非定常计算的每一个时间步,首先通过基于压强梯度的流场探针识别出激波所在位置,然后对激波附近点云进行加密,从而提高对激波的分辨率,同时对远离激波的点云进行粗化,尽可能减少冗余节点,提高计算效率。采用所提出的无网格自适应算法求解了N-S方程,首先对一维运动激波问题进行了数值模拟,通过将数值模拟结果与精确解比较,验证了所提算法求解存在运动激波的非定常流动的可行性,在此基础上,将方法推广用于二维非定常流动问题的求解,分别对瞬时激波碰撞圆柱以及双弧翼型激波振荡流动进行了数值模拟,计算结果表明,方法可以显著提高对激波的分辨率,同时相对于直接采用较密布点的非自适应算法,自适应算法在计算效率上具有优势。

英文摘要：

In this paper,the gridless adaptive method is extended to simulate unsteady flows with moving shocks.In order to capture moving shocks with local high resolution,a technique of dynamic cloud of points is achieved by adopting clouds refinement and clouds coarsening procedures during the evolution of unsteady flows.The regions for clouds refinement and clouds coarsening are first determined by an indicator,which is defined as a function of the local pressure gradient,then the clouds refinement is carried out by introducing new points based on the existing structure of cloud of points,and the clouds coarsening procedure is also implemented simultaneously in order to control the size of the points distributed in the whole computational domain.The accuracy and efficiency of the presented gridless adaptive method are first validated by simulating unsteady inviscid flows including an incident shock past a cylinder,and then it is extended to simulate a self-excited unsteady flow over a circular-arc airfoil.The numerical results show that the gridless adaptive method presented can capture moving shocks with high resolution successfully in a way of dynamic adaptation of cloud of points.