Developing high-order weighted compact nonlinear schemes. (English) Zbl 0988.76060

Deng, Xiaogang; Zhang, Hanxin

J. Comput. Phys. 165, No. 1, 22-44 (2000).

The authors consider compact high-order nonlinear schemes and three fourth- and fifth-order weighted compact nonlinear schemes (WCNS). Using Fourier analysis, the authors discuss dissipative and dispersive features of WCNS. In view of the modified wave number, the WCNS are equivalent to fifth-order upwind biased explicit schemes in smooth regions, and both flux difference splitting and flux vector splitting methods can be applied to them, though they are finite difference schemes. Numerical results show a good performance of WCNS for discontinuity capture, high accuracy for boundary-layer calculations, and also a good convergence rate.

Reviewer: Qin Mengzhao (Beijing)

MSC:

76M20	Finite difference methods applied to problems in fluid mechanics
76N15	Gas dynamics (general theory)
76L05	Shock waves and blast waves in fluid mechanics

Keywords:

fourth- and fifth-order weighted compact nonlinear schemes; fifth-order upwind biased explicit schemes; schock wave; Navier-Stokes equations; Fourier analysis; flux difference splitting; flux vector splitting; convergence

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