格心型有限体积法格点变量重构方法研究  

Research on vertex variables reconstruction for cell-centered finite volume method

作　　者：张帆[1,2] 刘君[3] 陈飙松[1,2] 钟万勰[1,2] 

机构地区：[1]大连理工大学工程力学系,辽宁大连116024 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 [3]大连理工大学航空航天学院,辽宁大连116024

出　　处：《大连理工大学学报》2015年第5期449-456,共8页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(91315302);"九七三"国家重点基础研究发展计划资助项目(2010CB832704)

摘　　要：根据网格格点变量计算单元变量梯度是二阶空间精度格心型有限体积法梯度重构的常用方法,该方法的关键是根据格点的邻接单元格心变量构造满足局部线性分布的格点变量.采用加权最小二乘法进行格点变量重构,考虑实际格心变量的非线性分布,提出采用距离反比加权体现不同位置单元对格点变量的影响程度差异;针对扰动或弯曲网格中的格点变量重构出现极值的现象,采用了新的限制方法.采用高雷诺数边界层流动计算中常见的大长宽比、扰动/弯曲网格进行测试,将提出的方法与通常采用的加权平均方法和拟拉普拉斯方法进行对比.算例结果显示距离反比加权的最小二乘法重构精度较好,提出的限制方法避免了扰动/弯曲网格上的格点变量出现极值.A commonly-used gradient reconstruction procedure for the second-order cell-centered finite volume method is to calculate the element gradient by its vertex variables.The key issue of this method is to construct the local linearly distributed vertex variables by their adj acent elements＇ cell-centered variables. Using weighted least squares method for vertex variables reconstruction, considering the fact that the cell-centered variables are non-linear distribution,inversely distance weight is applied to estimate the different influences of the elements in various positions.In order to deal with the over-estimation of vertex variables on perturbed or curved grids,a new clipping method is implemented.Test cases use high-aspect-ratio,perturbed or curved grids which are commonly applied to the boundary layer flow simulations with high Reynolds number.The presented method is compared with weighted averaging method and pseudo-Laplacian method.Numerical results show that better accuracy is attained by presented inversely distance weighted least squares method,and the over-estimation of vertex variables on perturbed or curved grids is eliminated by the clipping method suggested here.

关 键 词：格心型有限体积法 梯度重构 格点变量 最小二乘法 限制方法 大长宽比网格 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]