改进最小二乘法的非结构网格梯度重构算法  

Gradient reconstruction of unstructured meshes based on improved least-squares method

作　　者：肖艺 明平剑[1] XIAO Yi;MING Pingjian(College of Power and Energy Engineering, Harbin Engineering University, Harbin 15001, China)

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

出　　处：《哈尔滨工程大学学报》2020年第12期1819-1826,共8页Journal of Harbin Engineering University

基　　金：国家自然科学基金项目(51206031、51479038);中央高校基本科研业务费重大项目(HEUCFP201711).

摘　　要：为了解决格心型有限体积法中,传统的加权最小二乘法(WLSQ)在大长宽比弯曲三角形/四边形网格存在较大梯度重构误差问题,本文研究了非结构化网格梯度重构方法。针对边界单元,在格林-高斯权重最小二乘法WLSQ(G)基础上采用共点型计算模板的距离反比加权的最小二乘法重构边界单元梯度,提出了BWLSQ(G)法。在自主开发的多物理场耦合软件GTEA基础上,完成二维圆环域稳态导热算例和大长宽比弯曲四边形/三角形网格测试。结果表明:提出的BWLSQ(G)有效提高了WLSQ(G)的计算效率,减小了边界单元梯度重构误差,达到一阶收敛精度。For the cell-centered finite volume method,the traditional weighted least-squares(WLSQ)method has a large gradient reconstruction error in large-aspect-ratio curved triangle/quadrilateral meshes.This study systematically investigated the unstructured grid gradient reconstruction method.Based on the Green-Gauss WLSQ(WLSQ(G))method for the boundary element,the BWLSQ(G)method was obtained by reconstructing the boundary element gradient via inverse distance weighting and stencil augmentation.Based on the self-developed multiphysics coupling software GTEA,the BWLSQ(G)performance was tested using a two-dimensional cylindrical steady-state thermal conductivity test,and the large-aspect-ratio and curved quadrilateral/triangle grid,respectively.The results showed that the improved BWLSQ(G)effectively improves the WLSQ(G)computational efficiency and reduces the boundary element gradient reconstruction error,and achieves the first-order convergence accuracy.

关 键 词：格心型有限体积法 梯度重构 最小二乘法 格林-高斯法 大长宽比弯曲网格 GTEA软件 非结构网格 

分 类 号：TK402[动力工程及工程热物理—动力机械及工程]