A multiple-time-step technique for coupled free flow and porous medium systems

A mass conservative multirate time integration method is developed for a time-dependent isothermal single-phase free flow system coupled with an isothermal single-fluid-phase porous medium system. Long time stability of the proposed numerical scheme is proved under a time step restriction which depends on the physical parameters of the flow systems and the ratio between the time steps applied in the free flow and porous medium domains. Convergence analysis is carried out and a priori error estimates are obtained. Numerical results are presented for two model problems and a realistic setup. Advantages of using multiple-time-step techniques for modeling coupled systems where the processes evolve on different time scales are demonstrated and discussed.