Minisymposium Presentation

Parallel-in-time algorithms offer a route to continued parallel scaling for simulation of space and time dependent partial differential equations once spatial parallelism is saturated. The equations relevant to geophysical fluid dynamics pose particular challenges for the convergence of parallel-in-time algorithms due to the hyperbolicity of the equations and the range of timescales spanned by the physical processes being modelled. In particular, weather and climate models depend on subgridscale parameterisations that describe physical processes that take place on scales that are not resolved by the dynamical partial differential equations in space or in time. These parameterisations often contain fast timescales and discontinuities, for example, it is commonly assumed in cloud parameterisations that the amount of water vapour above the saturation concentration is instantaneously converted into cloud droplets. In this talk I will present several parallel-in-time algorithms in the context of the shallow water equations, a commonly used equation set for the testing of new numerical algorithms relevant to weather and climate prediction. I will show how the equation set can be extended to include clouds, focussing on the challenges that this poses to convergence of parallel-in-time algorithms.