AUSM^+-up格式在无网格算法中的推广

Extending the AUSM^+-up scheme into the gridless method

将AUSM+-up格式推广运用到了无网格算法中。在点云离散的基础上,运用曲面拟合和AUSM+-up格式求得数值通量;采用四步龙格-库塔方法进行时间推进,并引入当地时间步长和残值光顺等加速收敛措施。为了验证本文方法的计算精度和鲁棒性,对NACA0012翼型跨声速流动、某三段翼型低速绕流、平行错位NACA0012双翼超声速、高超声速流动进行了数值模拟。

In this paper, the AUSM^＋-up scheme is extended into the gridless method. A quadrantal point infilling strategy is developed to generate point and combine clouds of points automatically. On the base of the distributed clouds of points, local least-squares curve fits and the AUSM^＋ -up scheme are used to obtain the numerical flux. An explicit multistage Runge-Kutta algorithm is used to advance the flow equations in time, at the same time local time stepping technique and residual averaging are employed to accelerate the convergence of solution. In order to demonstrate the accuracy and applicability of the method, the NACA0012 airfoil in transonic flow, multi-element airfoil complex flow and a pair of NACA0012 airfoils in supersonic and in hypersonic flow are computed.