基于制造解的非结构二阶有限体积离散格式的精度测试与验证

随着计算机技术的飞速进步,计算流体力学得到迅猛发展,数值计算虽能够快速得到离散结果,但是数值结果的正确性与精度则需要通过严谨的方法来进行验证和确认.制造解方法和网格收敛性研究作为验证与确认的重要手段已经广泛应用于计算流体力学代码验证、精度分析、边界条件验证等方面.本文在实现标量制造解和分量制造解方法的基础上,通过将制造解方法精度测试结果与经典精确解(二维无黏等熵涡)精度测试结果进行对比,进一步证实了制造解精度测试方法的有效性,并将两种制造解方法应用于非结构网格二阶精度有限体积离散格式的精度测试与验证,对各种常用的梯度重构方法、对流通量格式、扩散通量格式进行了网格收敛性精度测试.结果显示,基于Green-Gauss公式的梯度重构方法在不规则网格上会出现精度降阶的情况,导致流动模拟精度严重下降,而基于最小二乘(least squares)的梯度重构方法对网格是否规则并不敏感.对流通量格式的精度测试显示,所测试的各种对流通量格式均能达到二阶精度,且各方法精度几乎相同;而扩散通量离散中界面梯度求解方法的选择对流动模拟精度有显著影响.

ACCURACY VERIFICATION OF UNSTRUCTURED SECOND-ORDER FINITE VOLUME DISCRETIZATION SCHEMES BASED ON THE METHOD OF MANUFACTURED SOLUTIONS

With the great improvement in computer technology, computational fluid dynamics have progressed signifi-cantly. Even though it is fast and easy to obtain discretized results via numerical simulations, the validity and accuracy of the results need to be carefully validated and verified. As an important approach in verification and validation, the method of manufactured solutions (MMS) was widely applied in code verification, accuracy analysis and verification of boundary conditions. This paper first established the procedures for the MMS with scalar manufactured solutions and vector manufactured solutions. Verification of these two procedures was performed by comparing results of accuracy testing for a typical exact solution (2D inviscid isentropic vortex). The MMS procedures were then employed to the study of unstruc-tured finite-volume discretization schemes, such as gradient reconstruction methods, convective fluxes discretization and diffusive fluxes discretization. It demonstrated that some schemes employing certain Green-Gauss based gradient degrade to 1st order on irregular meshes and discretization error increases significantly, while the least squares based gradient is insensitive to mesh irregularity. Besides, all tested convective fluxes discretization schemes were 2nd order accurate and they exhibited similar performance in terms of accuracy. But the method of computing the interface gradient was an essential factor affecting the accuracy of diffusive fluxes discretization.