Fifth-order Z-type weighted essentially non-oscillatory schemes for hyperbolic conservation laws
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In this paper we propose the variant Z-type nonlinear weights in the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme for hyperbolic conservation laws. Instead of employing the classical smoothness indicators for the nonlinear weights, we take the pth root of the smoothness indicators and follow the form of Z-type nonlinear weights introduced by Borges et al., leading to fifth-order accuracy in smooth regions, even at the critical points, and sharper approximations around the discontinuities. We also prove that the proposed nonlinear weights converge to the linear weights as p →∞, meaning the convergence of the resulting WENO numerical flux to the finite difference numerical flux. Finally, numerical examples are presented to demonstrate that the proposed WENO scheme performs better than the WENO-JS, WENO-M and WENO-Z schemes in shock-capturing.
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