A third order central WENO scheme for 2D conservation laws

Abstract

We present a new third-order essentially non-oscillatory central scheme for approximating solutions of two-dimensional hyperbolic conservation laws. Our scheme is based on a two-dimensional extension of the centered weighted essentially non-oscillatory (CWENO) reconstruction we presented in Levy et al. [3]. This is a “true” 2D method; it is not based on a direction-by-direction approach. Our method is formalized in terms of a black box which needs as an input only the specific flux. The numerical results we present support our expectations for a robust and high-resolution method.