Fast-wave slow-wave spectral deferred correction methods applied to the compressible Euler equations

In numerical weather prediction and climate modelling, semi-implicit time-stepping methods have long been favoured for their ability to take large time steps without excessively damping slow-moving waves. Fast-Wave Slow-Wave Spectral Deferred Correction (FWSW-SDC) methods offer an attractive alternative, achieving arbitrary-order accuracy by iteratively solving a collocation problem, akin to implicit Runge-Kutta methods. Similar to semi-implicit methods, FWSW-SDC improves stability compared to fully explicit schemes, enabling large time steps while retaining accuracy. Additionally, the rich literature on parallel-in-time SDC methods presents opportunities for both parallelization within the correction process and across time steps.

In this poster, we extend prior work with FWSW-SDC from linear systems to the nonlinear compressible Euler equations, evaluating its potential for numerical weather prediction and climate modelling applications. We apply SDC methods to standard dynamical core test cases, including the non hydrostatic gravity wave, moist rising bubble, and baroclinic wave tests, to assess stability, accuracy, and computational performance. Finally, we explore the implementation of parallelisable SDC preconditioners in the FWSW framework.