非结构嵌套网格中的一种改进型径向基函数插值方法  

An Improved Radial Basis Function Interpolation Method in Unstructured Nested Grids

作　　者：靳晨晖 王刚[1] 陈鑫 周豪 Jin Chenhui;Wang Gang;Chen Xin;Zhou Hao(School of Aeronautics,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]西北工业大学航空学院

出　　处：《航空工程进展》2019年第5期681-690,共10页Advances in Aeronautical Science and Engineering

基　　金：国家自然科学基金(11772265);西北工业大学研究生创意种子基金(ZZ2019001)

摘　　要：非结构混合网格拓扑关系相对复杂,在嵌套边界区域进行流场信息插值传递容易有精度的损失。利用已知的解析函数作为插值样本,对线性插值(LINE)、距离倒数权重插值(WA)、逆二次径向基函数插值(IQ)、Wendland’s C2径向基函数插值四种方法的精度进行对比,筛选出精度较高的C2径向基函数;提出一种改进的C2径向基函数插值方法,通过调整径向基函数的作用半径来控制插值矩阵条件数,进而消除使用径向基函数插值在嵌套边界区域出现的数值奇性问题;选用MD30P/30N多段翼与三维AEDC典型外挂物分离模型对该插值方法进行验证。结果表明:改进后的径向基函数插值方法能够有效消除嵌套边界区域数值奇性,同时计算收敛速率更快,插值精度更高。The unstructured hybrid grid has complex topological relation,and is easy to generate the accuracy loss in nested grid while performing the flow field information interpolation.The known analytic function is taken as the interpolation sample to investigate the accuracy of line interpolation,weighted interpolation by reciprocal distance(WA),inverse quadratic radial basis function interpolation(IQ)and Wendland’s C2 radial basis function interpolation,which can obtain the C2 radial basis function with high accuracy.The improved radial basis function is proposed,which can adjust the radius of Wendland’s C2 radial basis function to control the condition number of interpolation matrix,so as to eliminate the numerical singularity in the nested boundary region of radial basis function interpolation.The MD30P/30N multi-segment wing and typical 3D AEDC plug-in separation model are selected to verify the proposed interpolation method.The results show that the improved radial basis function interpolation method can eliminate the numerical singularity in the nested boundary region,and has fast calculation convergence speed and high interpolation accuracy.

关 键 词：非定常效应 嵌套网格 径向基函数 数值奇性 矩阵条件数 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程] TG156[金属学及工艺—热处理]