A Fully—Implicit Semi—Lagrangian Hydrostatic Model of Atmospheric Dynamics

A fully-implicit semi-Lagrangian (FISL) hydrostatic grid-point model of atmospheric dynamics has been developed. The proposed FISL scheme is designed in a two time level, backward trajectory, horizontal semi-Lagrangian framework in which all dynamical processes other than horizontal advection, namely the vertical advection, gravity-wave propagation, and other leftover processes, are treated in a time-implicit manner. The FISL scheme is solved iteratively that includes a set of vertically-decoupled horizontally two-dimensional Helmholtz-type elliptic equations that are solved by a conjugate-residual algorithm. The scheme is stable for reasonably large Courant numbers. Preliminary results from numerical simulations of idealized three-dimensional baroclinic waves and two-dimensional mountain waves using the FISL hydrostatic model will be presented at the conference.