Mass-Conserving Implicit-Explicit Methods for Coupled Compressible Navier-Stokes Equations

TL;DR

This paper develops mass-conserving implicit-explicit coupling methods for the coupled compressible Navier-Stokes equations, addressing stability, accuracy, and efficiency in modeling air-sea interactions with interface conditions.

Contribution

It introduces novel IMEX coupling schemes that are proven to be mass conservative for coupled compressible Navier-Stokes systems under rigid-lid assumptions.

Findings

Numerical experiments demonstrate scheme stability.

Theoretical proof confirms mass conservation.

Methods effectively handle different time scales.

Abstract

Earth system models are composed of coupled components that separately model systems such as the global atmosphere, ocean, and land surface. While these components are well developed, coupling them in a single system can be a significant challenge. Computational efficiency, accuracy, and stability are principal concerns. In this study, we focus on these issues. In particular, implicit-explicit (IMEX) tight and loose coupling strategies are explored for handling different time scales. For a simplified model for the air-sea interaction problem, we consider coupled compressible Navier-Stokes equations with an interface condition. Under the rigid-lid assumption, horizontal momentum and heat flux are exchanged through the interface. Several numerical experiments are presented to demonstrate the stability of the coupling schemes. We show both numerically and theoretically that our IMEX coupling methods are mass conservative for a coupled compressible Navier-Stokes system with the rigid-lid condition.