Local and parallel efficient BDF2 and BDF3 rotational pressure-correction schemes for a coupled Stokes/Darcy system

Abstract

In this paper, the local and parallel two- and three-step backward differentiation formula (BDF2/BDF3) rotational pressure-correction schemes are developed for a coupled Stokes/Darcy system. The central advantage of these schemes is a time-dependent version of domain decomposition by solving the Stokes problem and Darcy problems in their respective domain. By following a similar idea in Guermond et al. (2005), the Stokes problem is solved by a vector-valued elliptic equation and a scalar Poisson equation per time step. The whole system can be composed of three simple linear equations that consume almost the same computational time. Thus, the presented methods can be efficiently applied with less communication requirements and has good parallelism. In theorey, we prove the unconditional stability and long-time stability of the BDF2/BDF3 rotational pressure-correction schemes for the coupled Stokes/Darcy system. Furthermore, some numerical experiments are presented to show the accuracy and efficiency of these schemes in terms of numerical convergence rates and reservoir engineering.