非结构网格质量对梯度重构及无粘流动模拟精度的影响

发布时间：2018-06-03 16:38

本文选题：非结构网格 + 梯度重构方法　；参考：《计算力学学报》2017年05期

【摘要】：综合利用理论分析和数值测试手段,研究了非结构格心型有限体积离散中梯度重构算法的计算精度,分别给出了非结构算法中常用的基于Green-Gauss公式(GG方法)和基于Least squares方法(LSQ方法)的梯度重构方法达到至少一阶精度的条件。其中,GG方法在面积分低阶项不能互相抵消的情况下,要求面心插值精度达到至少二阶;而LSQ方法对于任意网格均能实现梯度重构一阶精度。在各向同性网格上的梯度重构精度数值测试验证了数学推导结论;进一步通过制造解方法量化无粘流动数值离散误差,结合网格收敛性测试研究了网格质量(网格点随机扰动、网格弯曲度和网格倾斜度等因素)以及网格类型(三角形和四边形)对无粘流动模拟精度的影响,验证了理论分析结论。
[Abstract]:The computational accuracy of gradient reconstruction algorithm in finite volume discretization of unstructured lattice type is studied by means of theoretical analysis and numerical test. The condition that the gradient reconstruction method based on Green-Gauss formula GG method and Least squares method can achieve at least one order accuracy is given respectively. The GG method requires at least second order interpolation accuracy when the area can not offset each other, while the LSQ method can achieve the first order accuracy of gradient reconstruction for any mesh. The numerical test of gradient reconstruction accuracy on isotropic mesh verifies the conclusion of mathematical derivation, and further quantifies the numerical discrete error of inviscid flow by manufacturing solution method, and studies the mesh quality (grid point random perturbation) by combining with the mesh convergence test. The influence of factors such as mesh curvature and mesh inclination and mesh type (triangle and quadrangle) on the accuracy of the simulation of non-viscous flow is verified.
【作者单位】：中国空气动力研究与发展中心计算空气动力研究所;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;
【基金】：国家自然科学基金(11532016)资助项目
【分类号】：O35

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