Euler方程无网格算法在可压缩流场中的应用

Gridless Method for Compressible Euler Equations

无网格算法区域离散用"点云"代替传统的网格算法中的网格划分。在当地点云上,引入二次极小曲面逼近计算空间导数,离散的Euler方程运用五步Runge-Kutta法直接推进求解。文中将非结构网格上的守恒型耗散算子直接应用到无网格方法中,计算域内点的生成借鉴成熟的结构网格和非结构网格生成技术,点云的选取快速而方便。最后,运用该方法给出了几个典型的算例。

The 2D Euler equations are solved with the explicit gridless method ,which uses only clouds of points and does not require that the points be connected to form a grid as in conventional CFD algorithms. The spatial derivatives of the Euler equations are estimated with a least-square curve fit on local clouds of points. Five steps of Runge-Kutta are adopted for time-marching to solve a discrete form for Euler equations. The conservative dissipation operator in the unstructured grids was extended to the gridless method,and points generation in the computational domain was in virtue of the ripe generation technique of structured and unstructured grids,and selection of clouds of points was fast and convenient. At last, several standard numerical results were obtained with the method presented.