Fully Implicit Numerical Methods for the Baroclinic Primitive Equations

A fully implicit code was developed to solve the three-dimensional primitive equations of atmospheric flow. The scheme is second order accurate in time and fourth order accurate in the horizontal and vertical directions. Furthermore, as a result of being fully implicit, the time step is not restricted by the mesh spacing near the poles, nor by the speed of inertia-gravity waves. Rather, the time step, deltat is determined simply by the requirement that it be small enough to adequately resolve the atmospheric flow of interest. The accuracy and efficiency of current models for fine grids should be significantly improved.