An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws

We develop in this article an improved version of the fifth-order weighted essentially non-oscillatory (WENO) scheme. Through the novel use of higher order information already present in the framework of the classical scheme, new smoothness indicators are devised and we obtain a new WENO scheme with less dissipation than the classical WENO of Jiang and Shu [2], with the same computational cost, and a slightly better performance than the improved mapped version of Henrick et al [3]. We show that the enhancements of the new scheme come from its ability to assign substantially larger weights to discontinuous stencils than the previous versions of WENO. Numerical experiments with the linear advection of discontinuous functions and the one dimensional Euler system of equations are conducted to demonstrate the benefit of using this improved version of the WENO scheme for hyperbolic conservation laws.