L. Bonaventura et V. Casulli, A SEMIIMPLICIT SCHEME FOR THE BAROTROPIC PRIMITIVE EQUATIONS OF ATMOSPHERIC DYNAMICS, INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 7(1), 1997, pp. 63
The primitive equations of a barotropic atmosphere in isobaric co-ordi
nates are reformulated, in order to express the geopotential gradient
as a function of the pressure at the Earth's surface. Furthermore, the
free surface equation is written in conservative form. A finite diffe
rence, semi-implicit, semi-Lagrangian scheme in isobaric co-ordinates
is developed. The numerical scheme is mass conservative, is proven to
be stable and requires the solution of a single five-diagonal system.
Numerical simulations show that the model captures the main dynamical
features of large scale atmospheric motion.