自由节点差分法梯度计算模板寻点策略研究及验证

Study and Validation of Point-Finding Strategy for Free-Node Differential Gradient Computation Template

混合网格在网格交界面处,需要通过插值进行流场信息交换,会引入插值误差。在FN-FDM算法实现中,需要先计算各网格点的梯度,这一过程需要构造梯度计算模板。针对梯度计算模板构造问题,本文综合考虑距离、角度等几何因素,提出了几种不同的梯度计算模板寻点策略,并通过数值试验确定了具有较高计算精度和效率的策略。数值试验结果表明,采用本文提出的选点策略,重叠网格下FN-FDM的计算精度与结构网格下同阶差分格式的计算精度相当,最终得出最优选点方案,在一定程度上提高了数值计算效率。

The mixed grid needs to exchange flow field information through interpolation at the grid interface,which will introduce interpolation errors.In the FN-FDM algorithm,it is necessary to first calculate the gradients of each grid point,and this paper requires constructing a gradient calculation template.In response to the problem of constructing gradient calculation templates,this paper comprehensively considers geometric factors such as distance and angle,proposes several different gradient calculation template point finding strategies,and determines the strategy with high calculation accuracy and efficiency through numerical experiments.The numerical experimental results show that by using the point selection strategy proposed in this paper,the computational accuracy of FN-FDM under overlapping grids is the same as that of the same order difference scheme under structural grids,which improves numerical computation efficiency to a certain extent.