In this paper we analyze the stability of different coupling strategies for multidomain PDEs that arise in general circulation models used in climate simulations. We focus on fully coupled ocean–atmosphere models that are needed to represent and understand the complicated interactions of these two systems, becoming increasingly important in climate change assessment in recent years. Numerical stability issues typically arise because of different time-stepping strategies applied to the coupled PDE system. In particular, the contributing factors include using large time steps, lack of accurate interface flux, and single-iteration coupling. We investigate the stability of the coupled ocean–atmosphere models for various interface conditions such as the Dirichlet–Neumann condition and the bulk interface condition, which is unique to climate modeling. By analyzing a simplified model, we demonstrate how the parameterization of the bulk condition and other numerical and physical parameters affect the coupling stability and establish stability conditions for different coupling strategies.

在本文中，我们分析了在气候模拟中使用的一般环流模型中出现的多域PDE的不同耦合策略的稳定性。我们关注于代表和理解这两个系统的复杂相互作用所需要的完全耦合的海洋-大气模型，这在近年来的气候变化评估中变得越来越重要。数值稳定性问题通常是由于应用于耦合PDE系统的时间步长策略不同而引起的。特别是，影响因素包括使用较大的时间步长，缺少准确的界面通量以及单迭代耦合。我们研究了各种界面条件（例如Dirichlet-Neumann条件和体界面条件）耦合的海洋-大气模型的稳定性，这是气候建模所独有的。