A well-balanced multi-moment constrained finite volume method for nonhydrostatic atmospheric models

The exact discrete hydrostatic balance cannot be kept in general when the vertical momentum equation is discretized in atmospheric numerical models. In order to exactly balance the discrete vertical pressure gradient force and gravity force, a well-balanced multi-moment constrained finite volume method for nonhydrostatic atmospheric flow is developed by introducing a well-balanced numerical formulation, in which a numerical reconstruction of the gravity source term is conducted in terms of a thermodynamic reference state that satisfies the hydrostatic balance. One-dimensional benchmarks show that the well-balanced multi-moment constrained finite volume method can maintain the numerical error of the hydrostatic reference state up to machine round off with a coarse grid spacing and can well simulate the propagation of small perturbations even in case of initial small perturbation. Two-dimensional nonhydrostatic thermal bubble test further confirms its ability of simulating nonhydrostatic atmospheric motion accurately. The above numerical experiments have verified the well-balanced property and applicability of the well-balanced multi-moment constrained finite volume method, which provides a good reference for the development of nonhydrostatic atmospheric models.