A well-balanced fifth-order A-WENO scheme based on flux globalization

We construct a new fifth-order flux globalization based well-balanced (WB) alternative weighted essentially non-oscillatory (A-WENO) scheme for general nonconservative systems.The proposed scheme is a higher-order extension of the WB path-conservative centralupwind (PCCU) scheme recently proposed in [A.Kurganov, Y. Liu and R. Xin, J. Comput.Phys., 474 (2023), Paper No. 111773].We apply the new scheme to the nozzle flow system and the twolayer shallow water equations.We conduct a series of numerical experiments, which clearly demonstrate the advantages of using the fifth-order extension of the flux globalization based WB PCCU scheme.