变限积分的有限体积法解决对流扩散方程  

Solving convection-diffusion equation by using the finite volume method with variable limit integral

作　　者：张丽剑[1] 罗跃生[2] 张文平[1] 

机构地区：[1]哈尔滨工程大学动力与能源工程学院,黑龙江哈尔滨150001 [2]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2015年第3期427-431,共5页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(51206031;51479038)

摘　　要：针对一维对流扩散方程,基于变限积分的有限体积法,提出一种高精度全离散方法。该方法在控制体内对方程进行变限积分,引入变限因子,然后分别对上下限再进行积分,从而将微分方程转化为积分方程,最后运用插值的方法对目标函数进行近似代替。该方法提高了计算精度,结果得到一维的收敛精度。采用Fourier分析法证明了格式为条件稳定。最后给出了非稳态和稳态2种情况下的数值算例,验证了所提出的格式具有高精度和易于编程计算的优点。In this paper,the one-dimensional convection-diffusion equation using one-dimensional unsteady equations as an example figures out a new high precision fully discrete format that is based on the finite volume method with variable limit integral. This method first integrates the equation with variable limit integral in the control body and introduces a variable limit integral factor. After that it integrates the upper and lower limits to transform the differential equation into the integral equation and then uses the interpolation method to approximately replace the objective function. In this way,the accuracy of the diffusion term is improved,deriving the one-dimensional convergence precision. The Fourier analysis method is used to prove the conditional stability of formation. Finally,the numerical examples of non-stable and stable conditions are given to verify the advantages of high accuracy and the easiness of programming calculation.

关 键 词：变限积分 高精度 对流-扩散方程 Fourier分析法 非稳态 一维 

分 类 号：O551[理学—热学与物质分子运动论]