A high-order fully explicit flux-form semi-Lagrangian shallow-water model

A new approach is proposed for constructing a fully explicit third-order mass-conservative semi-Lagrangian scheme for simulating the shallow-water equations on an equiangular cubed-sphere grid. State variables are staggered with velocity components stored pointwise at nodal points and mass variables stored as element averages. In order to advance the state variables in time, we first apply an explicit multi-step time-stepping scheme to update the velocity components and then use a semi-Lagrangian advection scheme to update the height field and tracer variables. This procedure is chosen to ensure consistency between dry air mass and tracers, which is particularly important in many atmospheric chemistry applications. The resulting scheme is shown to be competitive with many existing numerical methods on a suite of standard test cases and demonstrates slightly improved performance over other high-order finite-volume models.