A semi‐implicit scheme for the barotropic primitive equations of atmospheric dynamics

Abstract

The primitive equations of a barotropic atmosphere in isobaric co‐ordinates 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 difference, 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.

Citation

Bonaventura, L. and Casulli, V. (1997), "A semi‐implicit scheme for the barotropic primitive equations of atmospheric dynamics", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 7 No. 1, pp. 63-80. https://doi.org/10.1108/09615539710156200