CFD空间精度分析方法及4种典型畸形网格中WCNS格式精度测试  

Method for evaluating spatial accuracy order of CFD and applications to WCNS scheme on four typically distorted meshes

作　　者：涂国华[1] 邓小刚[2] 闵耀兵[1] 毛枚良[3] 刘化勇[1] 

机构地区：[1]中国空气动力研究与发展中心空气动力学国家重点实验室,四川绵阳621000 [2]国防科学技术大学,湖南长沙410073 [3]中国空气动力研究与发展中心计算空气动力研究所,四川绵阳621000

出　　处：《空气动力学学报》2014年第4期425-432,共8页Acta Aerodynamica Sinica

基　　金：国家重点基础研究发展计划项目(2009CB723800);国家自然科学基金(11072259)

摘　　要：计算流体力学中的精度阶数体现的是数值解随着网格加密向精确解收敛的速度,计算格式、网格质量和边界处理等都会影响计算精度。5阶非线性加权紧致格式(WCNS-E-5)是一种具有较高的精度和分辨率的有限差分格式,对强激波和复杂网格的适应性强。但是,格式的模板自适应选择器和网格的复杂性等都会对最终计算精度造成影响。为了分析精度,首先给出了两种通过数值解反推计算格式精度的方法:一种方法适合已知精确解的情况,另一种方法适合未知精确解的情况。然后在斜交网格、拉伸网格、拐折网格和扭曲网格等4种典型畸形网格中考察了WCNS-E-5格式的精度,考察算例涉及线性波动问题、等熵涡传播问题和超声速边界层问题等。计算结果表明WCNS-E-5在这四种网格中都体现出高阶精度。Accuracy order of computational fluid dynamics represents the grid convergence rate of numer-ical results towards exact physical results.Accuracy order may be affected by numerical schemes,grid quali-ty,boundary treatments,etc.Fifth-order Weighted Compact Nonlinear Scheme （WCNS-E-5）is a high reso-lution finite difference scheme and the robustness in capturing strong shock waves and high endurance in low quality grids has been shown.However,the adaptive weighted methods with smoothness indicators and the grid quality may degrade numerical accuracy.In order to find out the ultimate accuracy when grid distortion and boundary treatments are involved,two inversion formulas are derived by analyzing numerical solutions of partial difference equations.One formula is suited to the condition where exact solutions are available;the other is suited to the condition where exact solutions are unknown.The accuracy order of WCNS-E-5 is eval-uated on four typically distorted meshes：oblique crossed meshes,stretched meshes,cornered meshes and skewed meshes.WCNS-E-5 shows high order property on the four distorted meshes for the tested bench-mark problems including linear waves,an isentropic vortex,and a hypersonic boundary layer.

关 键 词：WCNS高阶精度 复杂网格 网格收敛性分析 边界格式 

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]