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

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.


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