一种基于面元梯度重建的格心型有限体积空间离散方法  

Spatial discretization algorithm for cell-centered finite volume method based on face gradient reconstruction

作　　者：魏雁昕 刘君[1] WEI Yanxin;LIU Jun(School of Aeronautics and Astronautics,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学航空航天学院,大连116024

出　　处：《航空学报》2024年第1期210-234,共25页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(11872144)。

摘　　要：梯度重构过程决定了有限体积法的空间离散精度和鲁棒性,针对二阶格心型有限体积法,研究并提出了一种新型梯度重构方法。该方法基于加权最小二乘原理,首先计算确定面元中心的变量值和变量梯度,然后针对不同网格类型分别使用中心差分、算术平均的方法求解单元格心变量梯度,在此基础上将边界条件与梯度重构过程相结合,发展了适配新方法的边界约束算法。利用精确测试函数进行网格收敛性研究,证明本文方法在光滑解条件下可以实现全场梯度的线性精确,一系列的无黏和黏性流动算例验证表明,相较于传统方法,本文方法可以有效降低近边界区域的数值耗散,提高计算精度,同时在大长宽比三角形网格条件下也具有良好的鲁棒性。The gradient reconstruction process determines the spatial discretization accuracy and robustness of the fi⁃nite volume method.A novel gradient reconstruction method is proposed for the cell-centered finite volume method.Based on the weighted least squares principle,this method calculates the face-centered variables and the gradient of these variables and then solves the cell-centered gradient using either central difference or arithmetic averaging meth⁃ods for different grid types.Finally,a new boundary constraint algorithm adapted to the new gradient reconstruction method is developed by combining boundary conditions with the gradient reconstruction process.A grid convergence study using an exact test function shows that the new method can achieve the linear reconstruction of the full-field gra⁃dient under smooth solution conditions.A series of inviscid and viscous flow cases show that,compared with the pre⁃vious method,this method can effectively reduce the numerical dissipation in the near boundary region and improve the computational accuracy with better robustness under the large aspect ratio triangular grid.

关 键 词：有限体积法 最小二乘法 梯度重构 边界约束重构 虚拟单元 

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]