基于空间嵌套径向基函数的高效并行网格变形方法  

An efficient parallel mesh deformation technique based on spatially-nested radial basis functions

作　　者：路宽 宋文萍[1,3] 郭恒博 叶坤 王跃[1,3] 韩忠华 LU Kuan;SONG Wenping;GUO Hengbo;YE Kun;WANG Yue;HAN Zhonghua(School of Aeronautics,Northwestern Polytechnical University,Xi’an 710072,China;AVIC Shenyang Aircraft Design and Research Institute,Shenyang 110035,China;National Key Laboratory of Aircraft Configuration Design,Xi’an 710072,China)

机构地区：[1]西北工业大学航空学院气动与多学科优化设计研究所,西安710072 [2]中国航空工业集团沈阳飞机设计研究所,沈阳110035 [3]飞行器基础布局全国重点实验室,西安710072

出　　处：《航空学报》2024年第15期206-217,共12页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(12072285)。

摘　　要：高效的网格变形方法可以大幅提高流固耦合数值模拟、基于高精度计算流体动力学(CFD)分析的气动外形优化设计等问题的计算效率。常规的基于径向基函数(RBF)的网格变形方法在变形控制点增多时,会引起网格变形计算量激增,而采用减少变形控制点的方法减小计算量,会带来拟合精度的损失。针对已有RBF网格变形方法计算效率与计算精度不能两全的现状,提出了一种空间嵌套径向基函数模型(SN-RBF),发展了基于SN-RBF模型的高效网格变形方法,在保证网格变形精度的同时大幅度提高了网格变形效率。发展的SN-RBF模型采用多个物理空间相互重叠的子模型代替样本点较多的径向基函数模型,大幅度缩短了径向基函数法网格变形的建模时间。鉴于其便于并行的优良特性,还发展了基于该网格变形方法的并行建模方法与并行网格变形方法,使得网格变形效率得到进一步提升。测试算例表明,建模样本点越多,网格变形效率提升越显著。其中CRM翼身组合体算例,建模效率提升高达16947倍,网格变形效率提升高达5218倍。Efficient mesh deformation methods can significantly improve computational efficiency in fluid structure interaction numerical simulation and aerodynamic shape optimization based on the high-fidelity CFD method.The mesh deformation method based on original Radial Basis Functions(RBF)can result in a significant increase in computational cost when the number of deformation control points increases.The method of reducing RBF modeling calculation time by reducing deformation control points can result in a loss of fitting accuracy.Since the existing deformation methods based on RBF cannot guarantee the computational efficiency and fitting accuracy simultaneously,this paper proposes a Spatially-Nested Radial Basis Function(SN-RBF)model and develops an efficient mesh deformation method based on SN-RBF.The proposed mesh deformation method maintains the accuracy of mesh deformation,while significantly improving the efficiency of mesh deformation.The spatially-nested radial basis function model utilizes multiple spatially overlapping sub models to replace the radial basis function model which has large number of deformation control points,greatly reducing the modeling time of RBF method in mesh deformation.Considering the good parallelism of the proposed method,the strategies for parallel modeling and parallel mesh deformation based on this method have been adopted,further improving the efficiency of mesh deformation.The test cases show that the more modeling sample points,the more significant the improvement in grid deformation efficiency.For the CRM wing-body configuration case,the maximum improvement in modeling efficiency is 16947 times,and the maximum improvement in mesh deformation efficiency is 5218 times.

关 键 词：径向基函数 空间嵌套径向基函数 网格变形 并行建模 

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]