Earth system models require efficient, accurate, and stable coupling schemes to enable partitioned solves of each of the component models. A common coupling strategy in climate models is for their components to exchange flux data from the previous time-step. This approach effectively performs a single step of an iterative solution method for the monolithic coupled system, which may lead to instabilities and loss of accuracy. This process can be viewed as “agnostic” coupling that does not utilize the structure of the problem. A better coupling strategy is to use a “well-informed” technique that leverages the structure of the specific problem to approximate the interface flux between components. The “well-informed” strategy isolates the interface flux in the problem, allows for special treatment of this quantity to improve its approximation. Furthermore, this strategy preserves the partitioned structure of the problem, allowing each model to be solved separately and simultaneously.
Traditional coupling schemes may develop instabilities and lead to unphysical simulation results. By using more accurate estimates of the interface flux, the proposed coupling approach avoids these pitfalls and increases the robustness of the coupled system simulations.
We formulate an Interface-Flux-Recovery (IFR) coupling method which improves upon the conventional coupling techniques in climate models. IFR starts from a monolithic formulation of the coupled discrete problem. The monolithic system is then enriched by treating the interface flux condition as an auxiliary equation. This allows for a separate treatment of the interface flux from each model. We then isolate the flux via a Schur complement to obtain an accurate approximation of the flux across the interface between the model components. This decoupling allows for independent solutions for each component using schemes that are optimized for each component, respectively. To demonstrate the feasibility of the method, we apply IFR to a simplified ocean-atmosphere model for heat-exchange coupled through the so-called bulk condition, common in ocean-atmosphere systems. We then solve this model on matching and non-matching grids to estimate numerically the convergence rates of the IFR coupling scheme.