Numerical simulations were performed on the massively separated flows of a 76/40° double delta wing using detached-eddy simulation(DES).A new type of cross-flow vortex is suggested.A vortex was initially generated near the junction of the strake and wing,which then moved towards the wing tip at certain wavelength and speed.Analyses were made in detail on the mechanism of the generation of the cross-flow vortex,that is,the inviscid cross-flow instability which differs from that of the swept blunt wing.Cross-section topology of the cross-flow vortex is also investigated,and the wavelength of the vortex array and the characteristic frequency are given.The analyses showed that the cross-flow vortices have an influence on the pressure distribution,which can cause a 10%-20% deviation from the averaged distribution.
The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes (WCNS) [Deng X. and Zhang H. (2000), J. Comput. Phys. 165, 22-44 and Zhang S., Jiang S. and Shu C.-W. (2008), J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. (2007), J. Sci. Comput. 31, 273-305 and Zhang S., Jiang S and Shu. C.-W. (2011), J. Sci. Comput. 47, 216-238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.
Shu-hai ZHANGXiao-gang DENGMei-liang MAOChi-Wang SHU
