Multirate partitioned Runge–Kutta methods for coupled Navier–Stokes equations

Abstract

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 multirate partitioned Runge–Kutta methods for the fluid–fluid interaction problem and demonstrates its parallel performance by using the PETSc library. 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.