计算流体力学中的验证与确认

计算流体力学(CFD)在航空航天等诸多领域的应用越来越广泛.特别是近年来, CFD在实际飞行器的设计中扮演着越来越重要的角色, 许多设计参数直接来源于CFD的计算结果.由此, 飞行器设计师对CFD提供结果的可信度提出了更高的要求.验证(verification)与确认(validation)是评价数值解精度和可信度的主要手段.本文综述了国内外开展CFD验证与确认研究的进展.在引言中论述了开展CFD验证与确认的重要性和必要性, 简述了国内外CFD验证与确认研究的历史和发展现状.第2节中讨论了CFD验证与确认的一些基本概念,以及这些概念定义的形成过程, 并指出了进行CFD验证与确认的基本步骤.第3节和第4节分别讨论了CFD验证与确认的方法, 如CFD验证中的精确解比较方法, 制造解比较方法, 网格收敛性研究;CFD确认中的层次结构, 流动分类法, 确认实验指南.在第5节中我们列举了几个CFD验证与确认的应用实例.最后, 对我国开展CFD验证与确认研究工作提出了若干建议, 包括:(1)开展流动分类法研究,(2)推行软件质量工程方法,(3)开展规范精细的实验, 建立国内的网络数据库. 

VERIFICATION AND VALIDATION IN COMPUTATIONAL FLUID DYNAMICS

During the last two or three decades, computational fluid dynamics (CFD) hasbeen widely used in the scientific research and the analysis and design ofengineering systems. Especially in recent years, CFD has been playing a moreand more important role in the design of aeronautical and astronauticalvehicles. So many design conditions for realistic aircraft have beendetermined directly from the results of CFD. However, users and developersof CFD today face a critical question: How can the confidence in modeling andsimulations be critically assessed? Verification and validation (V{\&}V) ofCFD are the primary methods for building and qualifying this confidence. Inthis paper, the state of the art of V{\&}V of CFD is reviewed. In theintroduction, we first discuss the background and importance of V{\&}Vin CFD, and then review briefly the history of V{\&}V. Secondly, thebasic terminology and methodology of V{\&}V are discussed, including several fundamental concepts, the definitions and the basic processes.Section three discusses the primary processes and methods of verification,including analytic solution method, manufactured solution method and gridconvergence analysis. Section four discusses the primary processes andmethods of validation, including validation tier hierarchy, flowclassification, and some guidelines for validation experiments. In the fifthsection, several applications of verification and validation are presented,including the typical Lax problem solved by WENO scheme and our DWENOscheme, hypersonic flows over the hollow cylinder/truncated flare and sharpdouble cone configurations presented by P. Gnoffo, supersonic side-jetinteraction for an axissymmetric body. Finally, some comments aremade with respect to the development of V{\&}V of CFD in China: (1) theimportance of flow classification research, (2) on software quality assurance, (3)on the international academic activities and successfuldatabases, (4) on standardizing our experiment data and documents, andbuilding our own database for CFD validation, (5) on an organization to manage theissues of V{\&}V in China, (6) on the editorial policy on numericalaccuracy in related Chinese academic publications.