Abstract: According to the Liu's weighted idea, a space third-order WNND (weighted non-oscillatory, containing no free parameters, and dissipative scheme) scheme was constructed based on the stencils of second-order NND (non-oscillatory, containing no free parameters, and dissipative scheme) 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 does not 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 Hanxin'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°.

Key words: high-order scheme, numerical simulation, topological structure, limiting streamline of surface, Navier-Stokes equation, WNND scheme