A multi-timestep Robin–Robin domain decomposition method for time dependent advection-diffusion problems

Many physical processes present separated evolution time scales in different regions, such as windblown sand in the desert. The evolution of bed-surface locally affects the sandy- wind flow, which erodes the sand in turns, while few meters higher from the ground the airflow is almost stationary. This and other applications suggest to improve the overall computational efficiency by locally adapting the time advancing step to the evolution in each region. We propose a multi-timestep Robin-Robin domain decomposition method, which uses mutually proportional time steps, based on a predictor-corrector strategy, cou- pled with linear interpolation in time. The resulting algorithm is completely segregated. Several numerical tests, obtained by the finite volume code OpenFOAM, are reported to show its stability and convergence properties.