非结构网格质量对梯度重构及无粘流动模拟精度的影响

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。

Mesh quality effects on the accuracy of gradient reconstruction and inviscid flow simulation on isotropic unstructured grids

The accuracy of gradient reconstruction methods implemented in unstructured cell-centered finite-volume discretization schemes were analyzed both theoretically and numerically.Conditions were derived for methods based on the Green-Gauss formula (GG methods) and methods based on the least squares approach (LSQ methods) to achieve at least first-order gradient reconstruction.For GG methods,second-order approximation of surface midpoint value is required when no cancellation effect occurs.On the other hand,LSQ methods are at least first-order accurate on arbitrary unstructured grids.Numerical testing on gradient reconstruction accuracy verified the mathematical conclusions.Solution errors of inviscid flow simulation were quantified using the Method of Manufactured Solutions (MMS).Grid convergence studies were performed to examine the effects of mesh quality,such as mesh perturbation,curvature,skewness and mesh type on the accuracy of inviscid flow simulation.