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

24 Feb 2022  ·  Shinhoo Kang, Alp Dener, Aidan Hamilton, Hong Zhang, Emil M. Constantinescu, Robert L. Jacob ·

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.

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Numerical Analysis Numerical Analysis Computational Physics Fluid Dynamics 76N06, 65M08, 65L04