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Multirate Partitioned Runge-Kutta Methods for Coupled Navier-Stokes Equations

Earth system models are complex integrated models of atmosphere, ocean, sea ice, and land surface. Coupling the components can be a signiﬁcant challenge due to the diﬀerence in physics, temporal, and spatial scales. This study explores new coupling strategies for the ﬂuid-ﬂuid interaction problem based on multirate partitioned Runge–Kutta methods. We consider compressible Navier–Stokes equations with gravity coupled through a rigid-lid interface. Our large-scale numerical experiments reveal that multirate partitioned Runge–Kutta coupling schemes (1) can conserve total mass; (2) have second-order accuracy in time; and (3) provide favorable strong- and weak-scaling performance on modern computing architectures. We also show that the speedup factors of multirate partitioned Runge–Kutta methods match theoretical expectations over their base (single-rate) method.