稳态非线性热传导问题的比例边界有限元法  

Scaled Boundary Finite Element Method for Steady-State Nonlinear Heat Conduction Problem

作　　者：李庆华[1] 冯子超 陈莘莘[1] 孔祥禄 Li Qinghua;Feng Zichao;Chen Shenshen;Kong Xianglu(School of Civil Engineering and Architecture,East China Jiaotong University,Nanchang 330013,China;China Railway Harbin Group Co.,Ltd.,Harbin 150001,China)

机构地区：[1]华东交通大学土木建筑学院,江西南昌330013 [2]中国铁路哈尔滨局集团有限公司,黑龙江哈尔滨150001

出　　处：《华东交通大学学报》2023年第6期110-114,共5页Journal of East China Jiaotong University

基　　金：国家自然科学基金项目(12162014,12172131);江西省主要学科学术和技术带头人培养计划(20225BCJ22010)。

摘　　要：提出一种基于比例边界有限元法和Kirchhoff变换求解稳态非线性热传导问题的数值方法。为了消除导热系数随温度变化引起的非线性,引入Kirchhoff变换将非线性的偏微分控制方程简化为Laplace方程,因而可消除迭代计算。作为一种兼顾了有限元法和边界元法优势的半解析数值方法,比例边界有限元法只需在计算域的边界上划分网格且不需基本解。在变换空间采用比例边界有限元法求得高精度的数值解之后,借助Kirchhoff反变换可求得温度场。数值结果表明,所提的稳态非线性热传导问题分析方法是行之有效的。A new numerical algorithm is presented to solve steady-state nonlinear heat conduction problems by combining the scaled boundary finite element method and the Kirchhoff transformation.In order to eliminate the nonlinearity related to the temperature dependence of the thermal conductivity,the Kirchhoff transformation is utilized to convert the nonlinear partial differential governing equation into the Laplace equation,and therefore iterative computation can be avoided.As a semi-analytical numerical method that combines the advantages of finite element method and boundary element method,the scaled boundary finite element method only requires the boundary without fundamental solution to be discretized.After the numerical solutions with high precision in the transformation space are calculated by the scaled boundary finite element method,the inverse transformation is required to derive the temperature field.Several numerical examples are presented to verify that the proposed method is effective for steady-state nonlinear heat conduction problem.

关 键 词：比例边界有限元法 热传导 非线性 Kirchhoff变换 

分 类 号：O343[理学—固体力学] U8[理学—力学]