非线性热传导方程MLPG/RBF-FD无网格数值模拟  

Numerical Simulation for the Nonlinear Heat Conduction Equations Based on MLPG/RBF-FD Meshless Method

作　　者：吴泽艳 郑保敬[2] 叶永[2] 石小涛[1,2] WU Ze-Yan;ZHENG Bao-Jing;YE Yong;SHI Xiao-Tao(Hubei International Science and Technology Cooperation Base of Fish Passage,China Three Gorges University,Yichang 443002,China;College of Hydraulic&Environmental Engineering,China Three Gorges University,Yichang 443002,China)

机构地区：[1]湖北省鱼类过坝技术国际科技合作基地,宜昌443002 [2]三峡大学水利与环境学院,宜昌443002

出　　处：《工程热物理学报》2022年第1期164-172,共9页Journal of Engineering Thermophysics

基　　金：三峡库区生态环境教育部工程研究中心开放基金(No.KF2015-06);国家自然科学基金资助项目(No.11602129,No.11972216)。

摘　　要：结合无网格局部彼得洛夫-伽辽金(MLPG)方法和径向基函数有限差分(RBF-FD)无网格方法求解非线性热传导问题。MLPG方法属于弱式无网格方法,具有处理边界条件方便的优点,然而因其要做大量的插值、积分运算而计算效率偏低;RBF-FD无网格方法属于强式无网格方法,直接对微分算子进行数值离散,计算效率高,然而其边界条件的处理较复杂。将二者相结合,在求解域边界附近采用MLPG方法,其它区域采用RBF-FD无网格方法,则能扬长避短。介绍了MLPG方法和RBF-FD无网格方法的基本原理,将该混合方法用来求解非线性热传导方程,数值算例显示了方法的正确性和高效性。The meshless local Petrov-Galerkin(MLPG)method and the finite difference radial basis function(RBF-FD)meshless method are combined to solve the nonlinear heat conduction problem.MLPG method is a weak meshless method,which has the advantage of being convenient to deal with boundary conditions.RBF-FD meshless method is a strong meshless method,which directly discretes the differential operator numerically and has high computational efficiency.By combining the two methods,the MLPG method is used near the boundary of the solution domain,and the RBF-FD meshless method is used in other regions.The basic principles of MLPG method and RBF-FD meshless method are introduced,and the hybrid method is used to solve the nonlinear heat conduction equation.Numerical examples show the correctness and efficiency of the method.

关 键 词：非线性热传导 MLPG RBF-FD 无网格 数值模拟 

分 类 号：TK124[动力工程及工程热物理—工程热物理] O241[动力工程及工程热物理—热能工程]