一种二维Stefan反问题的数值求解算法  

A Numerical Solution Algorithm for Two-Dimensional Stefan Inverse Problem

作　　者：徐海民 毕传光[2] 金峰[3] 张辉[1] XU Hai-min;BI Chuan-guang;JIN Feng;ZHANG Hui(School of Energy and Environment,Southeast University,Nanjing,210096,China;Technology Center of Ministry of Science and Technology,Shanghai Meishan Iron and Steel Co.Ltd.,Nanjing,210039,China;School of Energy and Power,Nanjing University of Aeronautics and Astronautics,Nanjing,210016,China)

机构地区：[1]东南大学能源与环境学院,江苏南京210096 [2]上海梅山钢铁股份有限公司科技部技术中心,江苏南京210039 [3]南京航空航天大学能源与动力学院,江苏南京210016

出　　处：《热能动力工程》2020年第5期209-216,共8页Journal of Engineering for Thermal Energy and Power

摘　　要：针对因相变引起边界位置移动的二维Stefan反问题,提出了基于有限体积法(FVM)结合Powell法的求解算法。首先假设待定边界位置的初始猜测值,采用Stefan正问题的无量纲化焓法模型,通过FVM对Stefan正问题进行计算,得到各测温点处对应的温度估计值,计算测量值和估计值的方差,然后采用Powell算法,通过方向置换准则判断搜索正确边界问题的方向向量。通过数值仿真实验对提出的算法进行了验证,讨论了测量误差、测点位置、初值、测量时刻数目以及测点数量对反演精度的影响,并与共轭梯度法(CGM)的反演结果进行了对比。数值实验结果表明,该算法能够精确地识别各种不规则的边界形状,并且对误差和初值等影响因素不敏感,具有良好的稳定性。Aiming at the two-dimensional Stefan inverse problem for boundary position movement caused by phase change,a solving algorithm based on finite volume method(FVM) combined with Powell method is proposed.Firstly,the initial value of the undetermined boundary position is assumed.The non-dimensioned enthalpy model with FVM is used to solve Stefan direct problem,and then the corresponding temperature estimation value at each temperature measurement point can be obtained.The variance between the measured value and the estimated value is calculated.The direction displacement criterion is used to determine the direction vector of the correct boundary problem by using the Powell algorithm.The proposed algorithm is verified by numerical simulation.The influences of measuring error,position of the measuring point,initial value,number of measuring moments and number of measuring points on the inversion precision are discussed.The inversion result of CGM is compared with that of Powell method.The numerical experiments show that the proposed algorithm can accurately identify various irregular boundary profiles and is insensitive to measurement errors and initial values.Hence,it has good stability in solving Stefan inverse problem.

关 键 词：导热反问题 STEFAN问题 相变 有限体积法 Powell法 

分 类 号：O241[理学—计算数学]