Predictor-Corrector in RAMSES with individual timesteps

[Philip Chang]

Dear RAMSES User/Developers,

I have a high level question about RAMSES's predictor-corrector method as applied to multiple time-steps. The questions is two fold.  

First, is there a paper which describes how RAMSES does second-order in time integration as applied to multiple timesteps. 

Second, (if there is no paper that describes this in detail), how does RAMSES do the predictor-corrector step when a cell, which has a timestep \Delta t, has a neighbor cell that has a timestep \Delta t/2.  In particular, I am interested in how the predictor step works in this case to guarantee conservation of conserved variables at machine precision (which assumes that all flux calculations are pairwise).  

The reason why I ask this is that I am interested in adapting the van-Leer time advance method to moving-mesh Voronoi methods with individual timesteps and patch-based AMR with individual timesteps are the closest thing to this.

Thanks. 

Cheers,

Phil Chang