Abstract: The application of basic function method in compressible viscous flowis discussed. By using first order trigonometric function as basic function, the central and upwind schemes of derivative are constructed. The technique of flux splitting method and the combination of central and upwind schemes are utilized to deal with the convection term of compressible Navior-Stokes equation. As for the viscosity term, only central scheme is used. A new basic function scheme for compressible viscous flowis constructed. Several numerical results of two examples for two dimensional and three dimensional axisymmetric compressible viscous supersonic steady flow illustrate the effectiveness of basic function method in dealing with compressible viscous flow.

Key words: basic function method, unstructured grid, compressible viscous flow

摘要： 研究基函数法在二维和三维轴对称情形下可压缩黏性流动中的应用, 并利用此法数值地计算了二维圆柱的超音速黏性绕流和三维球头的轴对称超音速黏性绕流两个算例。取一阶三角函数为基函数, 构造出导数的中心格式和迎风格式。对于可压缩N-S 方程中的对流项, 采用通量分裂法及中心格式与迎风格式相结合的技术;对于可压缩N-S方程中的黏性项, 则采用中心格式进行处理。由此, 构造出了数值求解黏性可压缩流动的一阶三角函数类型的基函数格式。两个算例的数值计算结果表明, 基函数法不仅在处理无黏可压缩流动时, 是一种高精度、高分辨率的新型计算方法, 而且在处理黏性可压缩流动问题时也一样行之有效。

关键词: 基函数法, 非结构网格, 黏性可压缩流动