A new 6th-order WENO scheme with modified stencils

Abstract

In this article, a new 6th-order weighted essentially non-oscillatory (WENO) scheme is developed. As with previous 6th-order central-upwind WENO schemes, the present scheme is a convex combination of four candidate linear reconstructions. The difference is that the most upwind and downwind stencils use four cell values, while the inner two stencils nominally use three cell values but the original quadratic reconstructions are modified to be 4th-order approximations by adding cubic correction terms involving the five cell values of the classical 5th-order WENO scheme. Sixth-order accuracy of the new scheme in smooth regions including critical points is achieved by using a reference smoothness indicator. Several numerical examples show that the new scheme has higher resolution compared with the recently developed 6th-order WENO schemes.