A Domain Decomposition Method for the Steady-State Navier--Stokes--Darcy Model with Beavers--Joseph Interface Condition

This paper proposes and analyzes a Robin-type multiphysics domain decomposition method (DDM) for the steady-state Navier--Stokes--Darcy model with three interface conditions. In addition to the two regular interface conditions for the mass conservation and the force balance, the Beavers--Joseph condition is used as the interface condition in the tangential direction. The major mathematical difficulty in adopting the Beavers--Joseph condition is that it creates an indefinite leading order contribution to the total energy budget of the system [Y. Cao et al., Comm. Math. Sci., 8 (2010), pp. 1--25; Y. Cao et al., SIAM J. Numer. Anal., 47 (2010), pp. 4239--4256]. In this paper, the well-posedness of the Navier--Stokes--Darcy model with Beavers--Joseph condition is analyzed by using a branch of nonsingular solutions. By following the idea in [Y. Cao et al., Numer. Math., 117 (2011), pp. 601--629], the three physical interface conditions are utilized together to construct the Robin-type boundary conditions on th...