基于局部解析解的非稳态导热计算  

Calculation of Heat Conduction Problem Under Cylindrical Coordinate System Based on Multi-Grid Method

作　　者：李江飞[1] 贺晓[1] 徐康泰[2] 翟克平 李智博[1] 罗璇[1] 邹振春[1] 王振业 Li Jiangfei;He Xiao;Xu Kangtai;Zhai Keping;Li Zhibo;Luo Xuan;Zou Zhencun;Wang Zhenye(Department of Thermal Engineering,Chengde Petroleum College,Chengde Hebei 067000,China;Dean's Office,Chengde Petroleum College,Chengde Hebei 067000,China;China Petroleum Pipeline Engineering Corporation,Langfang Hebei 065000,China)

机构地区：[1]承德石油高等专科学校热能工程系,河北承德067000 [2]承德石油高等专科学校教务处,河北承德067000 [3]中国石油天然气管道局管道工程有限公司,河北廊坊065000

出　　处：《科技通报》2017年第4期15-18,共4页Bulletin of Science and Technology

基　　金：承德市科学技术研究与发展计划项目(201602B016);河北省科技支撑项目(13211609)

摘　　要：针对圆柱非稳态导热问题,推导了基于局部解析解的有限容积法,利用Matlab编程进行求解,分析了计算结果。同时,还将基于局部解析解的有限容积法与中心差分法(二阶精度)有限容积方法的计算结果进行了对比。计算结果表明,网格数相同时,与二阶精度有限容积法相比,基于局部解析解的有限容积法计算量更大,计算精度更高。这是由于,基于局部解析解法的等效导热系数考虑了半径影响,使得精度提高。稳态解的比较中,有源项和导热系数分层时基于局部解析解法精度优势更加明显。The heat conduction equation of circular cylindrical coordinate system is a typical ellipticdiffusion equation.The value of each point in the computational domain affects each other in space.Based on multi-grid algorithm,the finite difference method is used to discrete the equations,thedistribution result of physical quantities is obtained when the flow reaches a steady state.Besides,thepaper also compares the result achieved by the Gauss and Seidel iterative method and analyzes thecalculation speed of two methods.The result shows that the multi-grid method can effectively increasethe calculation speed.Besides,selection of initial value has little impact on the multi-grid method andthe model has the preferable robustness.

关 键 词：非稳态导热 局部解析解 中心差分 有限容积法 

分 类 号：O414.14[理学—理论物理]