Fifth-order weighted essentially non-oscillatory schemes with new Z-type nonlinear weights for hyperbolic conservation laws

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