A new fifth order finite difference WENO scheme to improve convergence rate at critical points

Abstract

In the present work, we construct a new, improved version of fifth-order finite-difference Weighted Essentially Non-Oscillatory (WENO) scheme with less dissipation to approximate solutions for one- and two-dimensional hyperbolic conservation laws and associated problems. The higher-order information presented for the classical WENO scheme is applied to construct a new global smoothness indicator, a composition of first derivatives of local smoothness indicators with their respective interpolation polynomials. The sufficient condition of nonlinear weights is satisfied by using Taylor expansions. We verify the proposed scheme through several benchmark test cases for scalar and system of hyperbolic conservation laws. We observe from the numerical simulations that the designed WENO scheme demonstrates high resolutions, fifth-order accuracy, and robustness at critical points as compared with other modern WENO schemes.