Simulation of long time periods
 

All,

Does anyone have experience in simulating transient processes over long time periods (~1 million seconds). What are some thing to consider to reduce computational time?

The problem I'm looking at is for natural convection at a surface over long periods of time. The process is near steady state at short time scales, however the surface parameters change slowly over time.

One issue I have is to maintain a Courant number <1 the time step is 1e-3.
To be computationally feasible the time step should be >1 s.

Any advice is appreciated.