A New 8th-Order Central Upwind WENO Scheme

In recent years, the weighted essentially non-oscillatory scheme with high resolution and high accuracy has been developed. In this paper, an 8th-order upwind central Weighted Essentially Non-Oscillatory (WENO) scheme is proposed. The eight-order scheme selects five candidate stencils for reconstruction and convex combination, and adds a windward point to the last stencil to improve the stability. Since direct use of the classical JS weight can only lead to a 6th-order numerical scheme, we design a reference smoothness indicator to improve the accuracy. Several numerical examples suggest that the present scheme has stronger shock wave capture capability than the classical WENO schemes.