一种计算非定常二维流动的无网格算法

主要目的是发展一套求解非定常流动的无网格算法。计算区域的离散方面，提出了一种按区域进行填充布点的点云自动生成方法；发展了一种点云的运动技术来实现离散点云对物面边界的随体运动；在点云离散的基础上，采用最小二乘法求解矛盾方程的方法来求取空间导数，进而获得数值通量；采用双时间方法进行时间离散推进，其中物理时间迭代采用二阶隐式格式，伪时间迭代采用四步龙格一库塔显式格式，为了加速收敛，在伪时间迭代中采用了当地时间步长和隐式残值光顺等加速收敛措施。最后，利用本文算法模拟了NACA0012翼型和NACA64A010翼型的跨音速非定常流动，并将计算结果与实验测量结果进行了对比分析，验证了上述方法的正确性和实用性。

Gridless Solution Method for Two-Dimensional Unsteady Flow

The main purpose of this paper is to develop a gridless method for unsteady flow simulation. A quadrantal point infilling strategy is developed to generate point and combine clouds of points automatically. A point-moving algorithm is introduced to ensure the clouds of points following the movements of bodyboundaries. A dual time method for solving the two-dimensional Euler equations in Arbitrary Lagrangian-Eulerian (ALE) formulation is presented. Dual time method allows the real-time step to be chosen on the basis of accuracy rather than stability. It also permits the acceleration techniques, which are commonly used to speed up steady flow calculations, to be used when marching the equations in pseudo time. The spatial derivatives, which are used to estimating the inviscid flux, are directly approximated by using local least-squares curve method. An explicit multistage Runge-Kutta algorithm is used to advance the flow equations in pseudo time. In order to accelerate the solution to convergence, local time stepping technique and residual averaging are employed. The results of NACA0012 airfoil in transonic steady flow are presented to verify the accuracy of the present spatial discretization method. Finally, two AGARD standard test cases in which NACA0012 airfoil and NACA64A010 airfoil oscillate in transonic flow are simulated. The computational results are compared with the experimental data to demonstrate the validity and practicality of the presented method.