The advantage of WENO-JS5 scheme [ J. Comput. Phys. 1996] over the WENO-LOC
scheme [J. Comput. Phys.1994] is that the WENO-LOC nonlinear weights do not
achieve the desired order of convergence in smooth monotone regions and at
critical points. In this article, this drawback is achieved with the WENO-LOC
smoothness indicators by constructing a WENO-Z type nonlinear weights which
contains a novel global smoothness indicator. This novel smoothness indicator
measures the derivatives of the reconstructed flux in a global stencil, as a
result, the proposed numerical scheme could decrease the dissipation near the
discontinuous regions. The theoretical and numerical experiments to achieve the
required order of convergence in smooth monotone regions, at critical points,
the essentially non-oscillatory (ENO), the analysis of parameters involved in
the nonlinear weights like ϵ and p are studied. From this study, we
conclude that the imposition of certain conditions on ϵ and p, the
proposed scheme achieves the global order of accuracy in the presence of an
arbitrary number of critical points. Numerical tests for scalar, one and
two-dimensional system of Euler equations are presented to show the effective
performance of the proposed numerical scheme.Comment: 25 pages, 10 figure