In this paper, a new fifth-order weighted essentially non-oscillatory scheme for solving hyperbolic scalar conservation law is presented. This scheme is derived by using a three-point local stencils such as \(S0=\{I_{i-2},I_{i-1},I_{i}\}\) , \(S1=\{I_{i-2},I_{i-1},I_{i}\}\) and \(S2=\{I_{i},I_{i+1},I_{i+2}\}\) . A new reference smoothness indicator for the New WENO scheme is proposed by using reference value \(IS_{G5}\) based on lagrange interpolation on polynomials obtained from the global stencils \(\{I_{i-2},I_{i-1},I_{i},I_{i+1},I_{i+2}\}\) . It is constructed such that the sufficient condition on the weights for fifth-order convergence is satisfied. Analysis of accuracy of the New WENO scheme at critical points is discussed by comparing with WENO-JS and WENO-Z schemes. Furthermore, the numerical dissipation near discontinuities of the New WENO Scheme is discussed by comparing with WENO-JS and WENO-Z. The performance of the New WENO scheme is discussed with the help of several numerical experiments of one dimensional linear advection equation and one- and two-dimensional Euler equations. Numerical experiments shows that the New WENO scheme is less dissipative and perform higher resolution than the classical WENO-JS and WENO-Z scheme.
