Abstract
This paper develops a new hybrid finite difference scheme which consists of a nonlinear WENOCU4 scheme to maintain the numerical stability near discontinuities and a fourth-order linear central scheme elsewhere to accurately resolve smooth fluctuations and to speed up the computation. The central scheme is constructed in a robust skew-symmetric form which satisfies energy conservation property. A new efficient discontinuity detector is employed to identify the smoothness of the flowfield. As for the one-dimensional scalar equations, the hybrid scheme behaves almost no attenuation associated with propagation error. The quantitative analysis of the shock-capturing error is investigated. The hybrid scheme also exhibits high-resolution spectral property in the wavenumber space. Extensive cases of Euler equations further demonstrate the high-resolution shock-capturing ability of the detector, remarkable vortices-resolving capacity, and superior computational efficiency of the hybrid scheme. The reduced computational cost of the hybrid scheme is about 30−50% with respect to the baseline scheme.
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