非结构网格紧致高精度气体动理学格式

简要介绍了非结构网格上基于内自由度高效紧致重构方法的几种高精度气体动理学格式(GKS),包括结合三阶GKS通量求解器与子单元有限体积法(SCFV)及通量重构方法(CPR)构造的两种单步时空三阶格式SCFV-GKS和CPR-GKS,以及结合二阶GKS通量和两步四阶方法构造的时空四阶CPR-GKS。进而在CPR-GKS中混合SCFV增强对流场间断的分辨能力,并拓展到三维六面体网格。通过几种典型数值算例,对比分析了这几种格式在可压缩流动问题中具有的高精度、高效率和良好的间断捕捉能力。GKS通量的多维时空演化特性与紧致重构方法的高效性为发展高精度格式提供了有力的支撑。

Compact high-order gas-kinetic scheme on unstructured meshes

Several high-order accurate gas-kinetic schemes(GKS)on unstructured meshes are briefly introduced,which are based on the efficient compact reconstruction using inner degree of freedom.They include two single-step schemes with third-order accuracy in space and time,developed with the combination of third-order GKS flux solver and the subcell finite volume scheme(SCFV)or the correction procedure via reconstruction(CPR)framework,respectively.The third one is the two-step forth-order CPR-GKS which is developed with the simple second-order GKS flux and two-step forth-order method.A hybrid of SCFV is then conducted to enhance the resolution of flow discontinuities and the three-dimensional scheme is further constructed on hexahedral meshes.Several typical flows are simulated for the comparative study of their high accuracy,high efficiency and good capability of discontinuity capturing in compressible flows.The multidimensional space and time evolution of GKS flux,as well as the high efficiency of compact reconstruction provide strong support for the development of high order schemes.