LAUSR

In this paper, a marker and cell (MAC) scheme is constructed for the free flow-porous media system with heat transport on non-uniform grids, where the Stokes-Darcy equation is employed to describe the free-flow and the porous regions. Error estimates for the velocity, pressure and temperature in different discrete norms are established rigorously and carefully by constructing discrete auxiliary functions. We obtain the second order superconvergence in the discrete $$L^2$$ L 2 norm for velocity, pressure and temperature and the second order superconvergence for some terms of the $$H^1$$ H 1 norm for the velocity on non-uniform grids. Several numerical examples verifying the theoretical results and illustrating the capabilities of the method are demonstrated.