According to the Liu's weighted idea,a space third-order WNND scheme was constructed based on the stencils of second-order NND scheme.It was applied in solving linear-wave equation,1D Euler equations and 3D Navier-Stokes equations.The numerical results indicate that the WNND scheme which doesn't increase interpolated point(compared to NND scheme) has more advantages in simulating discontinues and convergence than NND scheme.Appling WNND scheme to simulating the hypersonic flow around lift-body shows:With the AoA(angle of attack) increasing from 0° to 50°,the structure of limiting streamline of leeward surface changes from unseparating,open-separating to separating,which occurs from the combined-point(which consists of saddle and node points).The separating area of upper wing surface is increasing with the AoA's increasing.The topological structures of hypersonic flowfield based on the sectional flow patterns perpendicular to the body axis agree well with ZHANG Han-xin's theory.Additionally,the unstable-structure phenomenon which is showed by two saddles connection along leeward symmetry line occurs at some sections when the AoA is bigger than 20°.
SHEN Qing,ZHANG Han-xin,GAO Shu-chun.A new upwind NND scheme for euler equations and its application to the supersonic flow[A].In: ZHANG Han-xin Ed.Proceedings of the Seventh China Computational Fluid Dynamics Conference[C].Chengdu:University of Electronic and Techndogy of China Press,1994,49—55.
Lynbimov A N,Rusanov V V. Gas flow past blunt bodies[R]. NASA-TT-F715，1973.
Hunt J C R,Abell C J,Peterka J A,et al. Kinematical studies of the flows around free or surface monuted obstacles,applying topology to vlow visualization[J].Journal of Fluid Mechanics,1978,86:179—200. doi: 10.1017/S0022112078001068