A parallel domain decomposition method for coupling of surface and groundwater flows

In this paper, we construct a robust parallel method based on a recently developed non-overlapping domain decomposition methodology to accurately model natural coupling of surface and groundwater flows. Stokes and Darcy equations are formulated and solved within the surface and subsurface regions, respectively. A new type of Robin–Robin boundary condition is proposed on the common boundary for the coupling of those systems. The formulation provides great flexibility for multi-physics coupling and is suitable for efficient parallel implementation. Meanwhile, it is stable with inherent system parameter variation. A numerical example is provided to verify the theory.