摘要
针对格心有限体积法的离散精度易受网格类型影响的问题,基于最小二乘原理,提出了一种适用于任意网格拓扑和网格质量的有限体积方法.在解的光滑区能保证二阶精度,可光滑、陡峭地捕捉激波等强间断面.精度与网格无关,且算法统一的特性使其非常适用于网格自适应和多重网格等计算应用,同时也降低了网格生成和流场求解的复杂性.跨音速算例的网格含有多种网格拓扑,计算结果表明发展的线性重构方法(linearreconstruction method,LRM)适用于不同的网格拓扑,计算得到的激波位置准确、陡峭,未产生数值振荡.运用Ringleb流动考查了该方法对低质量网格的收敛性,与传统方法相比,线性重构方法(LRM)不仅平均误差较小,而且误差随网格尺度的收敛性也更好,其精度接近二阶.三段翼型的黏性绕流计算进一步表明网格质量对其精度的影响较小.
A linear reconstruction method（LRM）,based on the least squares law,has been developed for cell-centered finite volume procedure in arbitrary grid type.The resolution and algorithm are independent of grid topology and quality.It does not suffer from a catastrophic loss of accuracy on a poor grid at the smooth region of solution.The shock can be captured in the absence of limiter.These advantages make it be easy in the application to the grid adaptation and multi-grid computations.In the transonic flow calculation, different grid topologies are included.Numerical results demonstrat the capabilities of new procedure for calculation of discontinuousness with different grid topologies.The data obtained are in good agreement with the experiments.The shock wave was obtained sharply,and non-physical vibration was avoided.Ringleb＇s flow is used to assess the accuracy in the low quality grids.Compared with the former reconstruction methods,the linear reconstruction method（LRM） is verified that the error norm is lower and the grid convergence is better. This character is further validated by calculation of viscous flow around tri-element airfoil.Relatively,the linear reconstruction method（LRM） obtained better data near the suction peaks.
出处
《力学学报》
EI
CSCD
北大核心
2010年第5期830-837,共8页
Chinese Journal of Theoretical and Applied Mechanics
基金
西北工业大学博士论文创新基金
国家自然科学基金(10872171
10802067)资助项目~~
关键词
网格拓扑
网格质量
有限体积法
线性重构方法
精度
grid topology
grid quality
finite volume
linear reconstruction method
accuracy
