中文摘要：

提出了基于三阶 WENO 重构的无网格算法，以期替代传统的无网格线性逼近重构，提高无网格算法的求解精度。基于无网格点云卫星点分布特征，通过沿点云中心点与卫星点连线方向引入局部一维坐标系，并结合虚拟点的设置，构成了在点云中实施三阶 WENO 重构所要求的模板。算法涉及的卫星点连线中点处的左右状态值，则利用模板上各点的流场值，采用 WENO 重构方法计算给出。对于模板中设置的虚拟点上的流场值，本文则利用已有的无网格点云信息，基于最近节点流场值插值得到。文中给出了采用上述 WENO 重构方法，结合 Roe 的近似Riemann 求解器确定通量，并采用三阶 TVD Runge-Kutta 方法进行时间推进求解 Euler 方程的具体实施过程。对模型问题的典型流动进行了计算分析，通过比较数值解和精确解，验证了算法获得的数值解能逼近三阶精度。给出的激波管流动和超声速半圆柱绕流算例展示出所发展的算法捕捉激波等间断问题具有更高分辨率，能体现出WENO 重构“基本无振荡”的特性。文中最后给出了非定常激波过弯道绕双圆柱流场的数值模拟算例，展示了所发展的算法处理含非定常激波演化的复杂流动问题的效果。

英文摘要：

In order to improve the accuracy of gridless method,the third-order WENO reconstruction is introduced as the substitution of traditional linear reconstruction.The stencil required for implementing WE-NO reconstruction in the gridless cloud is obtained by setting a local coordinate in the direction of each satel-lite point and introducing a virtual point.Based on the obtained stencil,the WENO reconstruction is then carried out for approximating the flow variables at the midpoint between the central and satellite points of the gridless cloud.An interpolation technique is also proposed to determine the flow variables of the virtual point,in which the existed information of the cloud is adequately utilized.The resulting WENO reconstruc-tion method,compiling with Roe’s Riemann solver for obtaining numerical flux and third-order TVD Runge-Kutta scheme for time advancing,is applied to solve Euler equations.Typical 2D cases are first simulated, and the numerical results obtained present the desired third order of accuracy.The shock tube problem and supersonic semi-cylinder flow are then simulated,and a higher resolution of shock and contact discontinuity is observed.The paper ends with numerical example of the flow field of shock wave through curved channel around double cylinders,which demonstrates the ability of the present method for treating more complicated flows involving unsteady shocks.