基于无网格稳定配点法的热传导问题分析  

Meshfree Stabilized Collocation Method for the Analysis of Heat Conduction Problem

作　　者：武凡舒 王莉华[1] 胡明皓 WU Fanshu;WANG Lihua;HU Minghao(School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2022年第4期844-854,共11页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11972261)。

摘　　要：本文引入一种新型无网格-稳定配点法求解热传导问题,这种方法采用重构核近似作为近似函数,在配点对应的子域内积分,能够满足积分高阶一致性条件,提高了配点型无网格法的精度和稳定性.一维到三维的数值算例均表明,与直接配点法相比,稳定配点法在求解热传导问题时能够显著提高精度,而且收敛稳定.In this paper, a new meshfree stabilized collocation method is introduced to solve the heat conduction problem. The reproducing kernel approximation is utilized as the approximation function in the presented method. The integration in the subdomain corresponding to the collocation point can satisfy the higher order consistency conditions in the integration form, which improves the accuracy and stability of the point collocation method. Numerical examples from one-dimensional to threedimensional show that, compared with the direct collocation method, the stabilized collocation method can significantly improve the accuracy in solving the heat conduction problems, with stable convergence.

关 键 词：稳定配点法 重构核近似 热传导问题 直接配点法 

分 类 号：TU311.4[建筑科学—结构工程] O241.82[理学—计算数学]