This page records the current state of a little project of the Azimuth code project, to develop a little climate model of our own, and collects useful references.

Details

In a first approximation a climate model is computational fluid dynamics on a rotating sphere, both atmosphere and oceans. So a climate model would need to solve an approximate version of the Navier-Stokes equations on the sphere with appropriate boundary conditions and an coupling between oceans and the atmosphere.

Solve the Burgers' equation with periodic boundaries in one (spatial) dimension. This would already include a lot of tools from numerical mathematics that would be needed to solve the Navier-Stokes equations in a 3D cube with periodic boundary conditions.

The 3D cube with periodic boundary conditions has been used as a model for turbulence, so that problem would probably be the next step.