An essential seventh-order weighted compact adaptive scheme for hyperbolic conservation laws (Q2666025)

The authors propose a hybrid seventh-order weighted compact scheme for hyperbolic conservation laws. The proposed reconstruction is inspired by the upwind compact scheme and the adaptive order weighted essentially non-oscillatory (WENO) scheme. The scheme is a convex combination of a linear seventh-order compact scheme and three linear third-order compact schemes. In addition, the reconstruction of this new scheme is based on the same stencil as the reconstruction of the original fifth-order weighted compact scheme. Several numerical tests are presented to show the efficiency of the method with respect to some existing high order methods for hyperbolic conservation laws.