Non-iterative domain decomposition methods for a non-stationary Stokes–Darcy model with Beavers–Joseph interface condition

In order to solve a non-stationary Stokes–Darcy model with Beavers–Joseph interface condition, two non-iterative domain decomposition methods are proposed. At each time step, results from previous time steps are utilized to approximate the information on the interface and decouple the two physics. Both of the two methods are parallel. Numerical results suggest that the first method has accuracy order O(h3+Δt)O(h3+Δt). In order to improve the accuracy and efficiency, a three-step backward differentiation is used in the second method to achieve an accuracy order O(h3+Δt3)O(h3+Δt3), which is illustrated by a numerical example.