两区域抛物方程耦合问题的二阶解耦算法

Second-order Partitioned Time Stepping Methods for a Parabolic Two Domain Problem

海洋与大气环流系统是通过海气交界面的相互作用而耦合在一起的,因此研究两区域两流体耦合模型的高效数值方法是非常重要的.本文针对两区域两个热传导耦合问题提出了两种二阶解耦算法.计算上,二者均实现了在每个时间层上独立求解一个热传导方程的目的,提高了计算效率,同时也简化了编程实现的难度;理论上,给出了两种方法的无条件稳定性和最优误差估计,另外数值结果也验证了理论分析结果的正确性.

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.