Numerical analysis of a second order algorithm for a non-stationary Navier–Stokes/Darcy model

In this paper, we construct a second order algorithm based on the semi-implicit spectral deferred correction method for the non-stationary coupled Navier–Stokes/Darcy equations with the Beavers–Joseph–Saffman’s interface condition. We present a complete theoretical analysis to prove that this algorithm is stable and possesses second order accuracy in time. Numerical examples confirm the convergence rate and the effectiveness of our algorithm.