Revisiting Implementations of the Finite Element Shallow Waetr Flow Model based on the Generalized Wave Continuity Equation in Spherical Coordinates

ADvanced Circulation (ADCIRC), a widely used massively-parallel finite element based solver for modelling tides and storm surge, is based on the shallow water equations in which the mass equation is reformulated into the Generalized Wave Continuity Equation (GWCE). For the governing equations in spherical coordinates, ADCIRC solves a set of equivalent equations in Cartesian coordinates arising from a coordinate transformation with an equidistant cylindrical projection. In this study, we revisit a spherical coordinate formulation and its numerical implementations especially of the GWCE. The formulation considers the the form of equations that is amendable to mass conservation, yields desirable numerical stability in the high latitude, is less intrusive in the implementation. Numerical performances of the revisiting formulation are demonstrated through global tides and regional tide solutions.