应用数学和力学2026，Vol.47Issue(5)：589-604,16.DOI:10.21656/1000-0887.460033
二维瞬态非线性热传导问题的数值流形法求解
A Numerical Manifold Method for Solving 2D Transient Nonlinear Heat Conduction Problems
摘要
Abstract
The numerical manifold method(NMM)effectively realizes the unified treatment of continuous and discontinuous problems through introduction of 2 cover systems:the mathematical cover for constructing the partition of unity functions and the physical cover for constructing the local approximation function.The appli-cation of the NMM to 2D transient nonlinear heat conduction problems was investigated.Firstly,based on the governing equations for the transient nonlinear heat conduction,along with the initial and boundary conditions,the weak form of the initial-boundary value problem was established.Subsequently,an NMM approximate ex-pression for the temperature field was presented and the global discretization form was derived with the Galer-kin method.For the time discretization,the backward Euler difference method was used and combined with the Newton-Raphson iterative method to solve the algebraic equations.From simulation of typical discontinuous plates with irregular boundaries and holes,the results show that,the NMM not only has high computational ac-curacy(the maximum error is not more than 0.6%)and good robustness,but also can handle complex geome-tries and discontinuous plates more effectively,which provides an innovative and efficient new method for nu-merical computation in this field.关键词
非线性热传导/数值流形法/Galerkin法/Newton-Raphson法/温度场Key words
nonlinear heat conduction/numerical manifold method/Galerkin method/Newton-Raphson method/temperature field分类
数理科学引用本文复制引用
张丽美,聂治豹,张楠,郑宏,赵帅星,杨龙..二维瞬态非线性热传导问题的数值流形法求解[J].应用数学和力学,2026,47(5):589-604,16.基金项目
云南省重点研发计划(202403AA080001) （202403AA080001）
国家电网有限公司总部科技项目(5200-202355156A-1-1-ZN) （5200-202355156A-1-1-ZN）
