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Based on the traditional fifth-order weighted essentially non-oscillatory(WENO)scheme,a smoothness indicator is introduced to improve the capability of WENO schemes for resolving short waves.In the construction of the new smoothness indicator,the proportion of the first-order term in the original smoothness indicator is reduced by replacing the square of the first-order term with the product of the first-order and the third-order terms.To preserve the fifth-order of convergence rate,the smoothness indicator is combined with the method of Borges,et al.The numerical results show that the proposed schemes are more suitable for simulating turbulent flows or aeroacoustics problems than the previous fifth-order WENO schemes,thanks to its improved resolution on short waves.
Based on the traditional fifth-order weighted essentially non-oscillatory (WENO) scheme, a smoothness indicator is introduced to improve the capability of WENO schemes for resolving short waves.In the construction of the new smoothness indicator, the proportion of the first-order term in the original smoothness indicator is reduced by replacing the square of the first-order term with the product of the first-order and the third-order terms. To preserve the fifth-order of convergence rate, the smoothness indicator is combined with the method of Borges, et al. Numerical results show that the proposed schemes are more suitable for simulating turbulent flows or aeroacoustics problems than the previous fifth-order WENO schemes, thanks to its improved resolution on short waves.