A fully-compressible nonhydrostatic cell-integrated semi-Lagrangian solver (CSLAM-NH) with consistent and conservative transport
A new semi-implicit fully-compressible nonhydrostatic CISL solver proposed here uses the Conservative Semi-Lagrangian Multi-tracer scheme (CSLAM; a CISL approach) as the transport scheme and uses a new flux-form formulation of the discrete semi-implicit continuity equation that ensures numerically consistent transport. The formulation is based on a recent successful approach used in the shallow-water equations solver, CSLAM-SW. The algorithm is constructed to be similar to typical conservative SLSI schemes, requiring at each time step a single linear Helmholtz equation solution and a single application of CSLAM. The new semi-implicit CISL solver is extended for the fully-compressible nonhydrostatic equations and tested for the desirable properties of local (and thus global) mass conservation, consistency, and shape-preservation of moisture variables and tracers. The formulation of the nonhydrostatic solver and results from several idealized dry and moist test cases will be presented.