二维功能梯度材料热传导格点型有限体积法研究  

Investigation on cell-vertex finite volume method for the heat conduction of two-dimensional functionally graded materials

作　　者：龚京风 徐宗著 宣领宽 江致远 郑文利 GONG Jingfeng;XU Zongzhu;XUAN Lingkuan;JIANG Zhiyuan;ZHENG Wenli(School of Automobile and Traffic Engineering,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]武汉科技大学汽车与交通工程学院,湖北武汉430065

出　　处：《哈尔滨工程大学学报》2023年第2期321-328,共8页Journal of Harbin Engineering University

基　　金：国家自然科学基金青年基金项目(51909197);湖北省自然科学基金项目(2019CFB136);武汉科技大学预研基金项目(GF201911)。

摘　　要：为了分析二维功能梯度材料热传导问题,发展格点型有限体积法,本文利用交错网格技术处理任意空间分布的材料物性,并使用C++语言开发数值求解程序。利用该程序分析不同网格类型下功能梯度材料圆环和不同边界条件下功能梯度材料板的热传导问题。结果表明:发展的格点型有限体积法对于线性三角形单元及双线性四边形单元的适用性良好,不同边界条件下格点型有限体积法解与解析解的误差不超过±0.12%,验证了求解程序的正确性。与有限元及解析解结果对比发现,当结构角点处存在剧烈温度变化且网格较为粗糙时,有限元结果出现数值振荡的现象,而格点型有限体积法结果仍然合理。分析表明:对于复杂的功能梯度材料热传导问题,格点型有限体积法比有限元方法具有更好的数值稳定性。To analyze the heat conduction problem of two-dimensional functionally graded materials(FGMs),the staggered cell-vertex finite volume method(CV-FVM)is developed in this research.Staggered grid technology is applied to process the material properties of arbitrary spatial distribution,and the C++language is used to develop the numerical solution program.This program is used to analyze the heat conduction of FGM rings under different grid types and FGM plates under different boundary conditions.The results show that the developed CV-FVM method has good applicability for linear triangular elements and bilinear quadrilateral elements.The error between the CV-FVM and analytical solutions under different boundary conditions does not exceed±0.12%,which verifies the correctness of the solution procedure.Comparing the finite element and analytical results shows that when severe temperature changes occur at the corners of a structure with a coarse grid,the finite element results exhibit numerical oscillations,but the CV-FVM results are still reasonable.The analyses indicate that compared with the complicated finite element method,CV-FVM has better numerical stability for complicated heat conduction analysis of FGMs.

关 键 词：交错网格 格点型有限体积法 二维功能梯度材料 热传导 数值振荡 C++程序语言 误差分析 CAE软件 

分 类 号：TK124[动力工程及工程热物理—工程热物理]