High Order Global Smoothness Indicator for Improving the Fifth- order Weno-z Scheme

Abstract eng:
Two new high-order (sixth- and seventh-order) global smoothness indicators of the 5-point stencil used in the fifth-order WENO scheme are proposed. Using the new smoothness indicators to construct the WENO-Z type scheme, the sufficient condition of the fifth order convergence for a fifth-order WENO is satisfied even at critical points where the first-order derivatives are zero. Compared with existing global smoothness indicators, two new indicators contain all terms in the smoothness indicators of three sub-stencils, and the maximal ratio of the coefficients of different first-order undivided differences (Ƹfi+1/2=fi+1-fi) is not greater than 3. Hence they can keep the property of essentially non-oscillation as well as low dissipation. Numerical results demonstrate the improved accuracy and robustness of the new WENO schemes.

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