Fuzzy finite difference method for heat conduction analysis with uncertain parameters  

作　　者：Chong Wang Zhi-Ping Qiu 

机构地区：[1]Institute of Solid Mechanics,Beihang University

出　　处：《Acta Mechanica Sinica》2014年第3期383-390,共8页力学学报（英文版）

基　　金：supported by the National Special Fund for Major Research Instrument Development(2011YQ140145);111 Project(B07009);the National Natural Science Foundation of China(11002013);Defense Industrial Technology Development Program(A2120110001 and B2120110011)

摘　　要：A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.

关 键 词：Heat conduction Fuzzy uncertainties Finitedifference method Parameter perturbation Stability analysis 

分 类 号：O551.3[理学—热学与物质分子运动论] TP75[理学—物理]