The 6th-order weighted ENO schemes for hyperbolic conservation laws

In this work, a 6th-order central-upwind weighted essentially non-oscillatory scheme is devised by additionally introducing a large stencil. The constrained condition of choosing this large stencil is that it should contain upwind information to raise the numerical stability of schemes. The implementation of scheme presented here is as compact as the classical weighted essentially non-oscillatory scheme. Several numerical examples show the robust and high-resolution performances of the scheme which is comparable with the recently developed 6th-order weighted essentially non-oscillatory scheme.