A global finite-difference semi-Lagrangian model for the adiabatic primitive equations

We develop a global semi-implicit semi-Lagrangian model for the atmospheric adiabatic primitive equations discretized through finite-differences. The model formulation includes a new semi-Lagrangian treatment of the continuity equation and a spatially averaged Eulerian handling of the orography. These techniques contribute to the accuracy and efficiency of the scheme. The semi-Lagrangian discretization makes the integration method very stable; we can carry out integrations with time-steps which by far exceed the CFL time-step limitations of Eulerian schemes. We carry out several numerical experiments, showing that good accuracy is achieved even when we triple the time-steps. Our numerical experiments also demonstrate the computational efficiency of the method; we can run 10 days simulations at fine resolutions in a few hours on a personal computer.