An improved fifth order alternative WENO-Z finite difference scheme for hyperbolic conservation laws

An alternative formulation of conservative weighted essentially non-oscillatory (WENO) finite difference scheme with the classical WENO-JS weights (Jiang et al. (2013) [6]) has been successfully used for solving hyperbolic conservation laws. However, it fails to achieve the optimal order of accuracy at the critical points of a smooth function. Here, we demonstrate that the WENO-Z weights (Borges et al. (2008) [1]) should be employed to recover the optimal order of accuracy at the critical points. Several one- and two-dimensional benchmark problems show the improved performance in terms of accuracy, resolution and shock capturing.