Numerical analysis of uncertain temperature field by stochastic finite difference method  

作　　者：WANG Chong QIU ZhiPing WU Di 

机构地区：[1]School of Aeronautic Science and Engineering, Beihang University [2]China Academy of Launch Vehicle Technology

出　　处：《Science China(Physics,Mechanics & Astronomy)》2014年第4期698-707,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.90816024,10872017 and 10876100);the Defense Industrial Technology Development Program(Grant Nos.A2120110001 and B2120110011);the 111 Project(Grant No.B07009)

摘　　要：Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters,initial and boundary conditions is discussed.Begin with the analysis of steady-state heat conduction problems,difference discrete equations with random parameters are established,and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method.Subsequently,the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed.The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming.Finally,by comparing the results with traditional Monte Carlo simulation,two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters,initial and boundary conditions is discussed.Begin with the analysis of steady-state heat conduction problems,difference discrete equations with random parameters are established,and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method.Subsequently,the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed.The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming.Finally,by comparing the results with traditional Monte Carlo simulation,two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.

关 键 词：heat conduction UNCERTAINTY stochastic finite difference parameter perturbation STABILITY 

分 类 号：TK124[动力工程及工程热物理—工程热物理]