Abstract: The atmosphere-ocean interaction can be modeled by a fluid-fluid system which coupled by some interface conditions. It is pretty important to study the robust numerical methods for the two domain coupling problem. In this paper, we study a simplified model of diffusion through two adjacent materials which are coupled across their shared interface. Two second-order partitioned time stepping schemes are proposed. Both schemes only require the solution of two decoupled parabolic problems at each time step. Hence, they are efficient in computation and can be easily implemented by using legacy codes. We also analyze their unconditional stabilities and convergence results, together with the numerical experiments, which verify our theoretical results.

Key words: parabolic two domain problem, partitioned time stepping method, stability