摘要
针对有限元求解瞬态温度场时解的振荡问题,通过对热传导矩阵和热容矩阵的分析,研究了数值仿真中解的振荡原因以及消除振荡的方法.研究结果表明,热传导矩阵违反了热力学第二定律,以及在迭代初期协调热容矩阵的单元内温度变化率的连续性假设与实际偏差很大是产生数值振荡的原因.规范单元形状和采用适当的集中热容矩阵,可以有效消除数值振荡.同时,以无限大平板传热过程为背景,通过不同计算方法的对比,验证分析了结论.
To overcome the numerical oscillation in solving transient temperature fields with the finite element method,the heat conduction matrix and the heat capacity matrix were analyzed,and the cause for the oscillation of numerical solution as well as the method of eliminating oscillation were studied. According to the results,the cause for the numerical oscillation is that the thermal conduction matrix violates the second law of thermodynamics,and at the beginning of the iteration,the continuity hypothesis of the temperature change rate of the elements in the heat capacity matrix is far from the actual situation. Regularization of element shapes and application of appropriate lumped mass heat capacity matrices can effectively eliminate the numerical oscillation. With an infinite plate in the heat transfer process as an example,the conclusion was verified through comparison between different calculation methods.
作者
刘文胜
李璇
马运柱
杨肃
LIU Wensheng;LI Xuan;MA Yunzhu;YANG Su(State Key Laboratory for Powder Metallurgy （ Central South University）, Changsha 410083, P.R. China)
出处
《应用数学和力学》
CSCD
北大核心
2018年第4期403-414,共12页
Applied Mathematics and Mechanics
基金
国家高技术研究发展计划(863计划)(2009AA034300)~~
关键词
瞬态温度场
有限元
振荡
热力学第二定律
集中热容矩阵
transient temperature field
finite element
oscillation
second law of thermody-namics
lumped mass heat capacity matrix
