一种新的计算非稳态流动的自适应无网格方法

基于带权点填充布点方法，结合指定流场参数梯度的分布，提出了一种新的无网格自适应方法计算非稳态问题。该方法的自适应探测器 E 由节点的权重和参数梯度组成。使用自适应探测器识别出加密或者粗化的区域，形成加密空腔和粗化空腔，然后重新填充布点。新节点的权重由自适应探测器 E 结合该处的梯度大小通过预测-校正迭代算法计算得到。另外，由于参数梯度在激波附近波动范围比较大，所以新节点的权重存在最大值和最小值。首先对预先设置压强梯度的流场区域进行自适应布点，并与传统自适应布点结果进行对比，点云分布图显示所提自适应方法重新生成的点云结构疏密分布更加合理。进一步，将此自适应方法应用于 Riemann 问题和激波碰撞圆柱问题，计算结果表明该方法可以在节点数目较低的情况下显著提高运动激波的分辨率。在激波碰撞圆柱问题中，比较了使用自适应算法和非自适应算法得到相当的结果所使用时间，前者是后者的20.6%，因此该自适应算法在计算效率方面也具有较大的优势。

A novel gridless adaptive method for simulating unsteady flows

Based on the weighted-point filling strategy,a novel gridless adaptive method is developed to capture shock waves with high resolutions in unsteady flows.The adaptive indicator E is the function of the local specified parameter gradients and the weight of points.The refining and coarsening regions are identified by the indicator,and then form refining cavities and coarse-ning cavities which are filled with new points.Using the predictor-corrector iterative algorithm, the weight of the new point is obtained by the adaptive indicator E and the local gradient.To pre-vent the violent change of the point weights with the parameter gradients,the maximum and the minimum are stipulated respectively in the filling process.The proposed adaptive method is first-ly used to fill points into the flow field which is set with designated pressure gradient in advance. By comparison with the traditional adaptive result,the sparse and dense distributions of clouds of points are more satisfactory and more reasonable.Further studies are the calculations of Riemann flow and incident shock past a cylinder.The results show that the adaptive method can capture the moving shock waves successfully in the unsteady flow fields with scanty points.For achieving equivalent pressure contours of the flow of the incident shock past a cylinder,the time spent using the presented adaptive method is 20.6% of the conventional unadaptive method,which suggests that it has a definite advantage on the computational efficiency.