An efficient low-dissipation hybrid central/WENO scheme for compressible flows. (English) Zbl 1500.76061
Summary: 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.
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:
hybrid finite difference scheme; nonlinear WENOCU4 scheme; numerical stability; fourth-order linear central scheme; energy conservation; shock sensor; Euler equations; high-resolution shock capturingReferences:
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