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 stencil 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°.
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References
Zhang Hanxin. On problems to develop physical analysis in CFD[A]. In: Zhang Hanxin ed.Proceedings of the Fourth Asian Computational Fluid Dynamics Conference [C], Mianyang, Chengdu, China, 2000,3–19.
Liu X D, Osher S, Chan T. Weighted essentially non-oscillatory schemes [J].Journal of Computational Physics, 1994,115:200–212.
Zhang H X, Zhuang F G. NND schemes and their applications to numerical simulation of two- and three-dimensional flows [J].Advances in Applied Mechanics, 1992,29(193):764–785.
Zhang Hang, Liu Jinhe, Guo Yijun. Study of flow topology with angle of attack change by simulating the hypersonic flow around blunt cone[A]. In: Zhang Hanxin ed.,Proceedings of the Seventh Separated Flows and Vortex Motion [C]. Beijing, China, 2002. (in Chinese)
Shen Qing, Zhang Hanxin, Gao Shuchun. A new upwind NND scheme for Euler equations and its application to the supersonic flow [A]. In: Zhang Hanxin. ed.,Proceedings of the Seventh China Computational Fluid Dynamics Conference [C]. Press of University of Electronic Science and Technology of China, Chengdu, 1994,49–55.
Lynbimov A N, Rusanov V V. Gas flow past blunt bodies [R]. NASA-TT-F715, 1973.
Zhang Hanxin. Cross flow topology of three-dimensional separated flows and vortex motion [J].Acta Aerodynamics Sinica, 1997,15(1):1–12. (in Chinese)
Zhang Hanxin, Deng Xiaogang. Analytical studies for three-dimensional steady separated flows and vortex motion [J].Acta Aerodynamics Sinica, 1992,10(1):8–20. (in Chinese)
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 flow visualization [J].Journal of Fluid Mechanics, 1978,86:179–200.
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Communicated by ZHANG Han-xin
Foundation item: the National Natural Science Foundation of China (90205013)
Biography: LIU Wei, Associate Professor, Doctor, E-mail: fishfather6525@sina.com
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Wei, L., Hai-yang, Z. & Yu-fei, X. Construction of third-order WNND scheme and its application in complex flow. Appl Math Mech 26, 35–43 (2005). https://doi.org/10.1007/BF02438362
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DOI: https://doi.org/10.1007/BF02438362
Key words
- high-order scheme
- numerical simulation
- topological structure
- limiting streamline of surface
- Navier-Stokes equation
- WNND scheme