非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进

非结构网格二阶有限体积离散方法广泛应用于计算流体力学工程实践中,研究非结构网格二阶精度有限体积离散方法的计算精度具有现实意义. 计算精度主要受到网格和计算方法的影响,本文从单元梯度重构方法、黏性通量中的界面梯度计算方法两个方面考察黏性流动模拟精度的影响因素. 首先从理论上分析了黏性通量离散中的“奇偶失联”问题,并通过基于标量扩散方程的制造解方法验证了“奇偶失联”导致的精度下降现象,进一步通过引入差分修正项消除了“奇偶失联”并提高了扩散方程计算精度;其次,在不同类型、不同质量的网格上进行基于扩散方程的制造解精度测试,考察单元梯度重构方法、界面梯度计算方法对扩散方程计算精度的影响,结果显示,单元梯度重构精度和界面梯度计算方法均对扩散方程计算精度起重要作用;最后对三个黏性流动算例(二维层流平板、二维湍流平板和二维翼型近尾迹流动)进行网格收敛性研究,初步验证了本文的结论,得到了计算精度和网格收敛性均较好的黏性通量计算格式. 

ACCURACY ANALYSIS AND IMPROVEMENT OF VISCOUS FLUX SCHEMES IN UNSTRUCTURED SECOND-ORDER FINITE-VOLUME DISCRETIZATION

Due to the widespread applications of unstructured second-order finite volume schemes in computational fluid dynamics (CFD) simulations, studying the discretization accuracy of second-order finite volume schemes is of practical value. Two primary factors that affecting accuracy of viscous flow simulation, including cell gradient reconstruction and interface gradient calculation method, are considered in this paper. Firstly, the odd-even decoupling problem in the discretization of viscous flux is analyzed theoretically and verified by the method of manufactured solutions (MMS) based on the scalar diffusion equation. Modification of interface gradient is proposed to eliminate the decoupling problem and the computational accuracy of the diffusion equation is improved greatly as a result. Then, the effects of cell gradient reconstruction and interface gradient method on the accuracy of viscous flow simulation are studied by the MMS method based on the diffusion equation. Results of MMS grid convergence tests show that cell gradient reconstruction and interface gradient method determine the accuracy of viscous flow simulation together. Finally, grid convergence tests are carried out for three realistic viscous flow cases, i.e., the laminar flat plate, the turbulent flat plate and the 2D airfoil near wake in NASA Turbulence Modeling Resource website. The numerical results verify the conclusions obtained by MMS tests, and the viscous flux discretization schemes are obtained with better performance in accuracy and grid convergence property.