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

TL;DR

This paper presents a high-order, robust spectral deferred correction method for the compressible Euler equations, demonstrating accurate, stable simulations for weather prediction models with extended physics parametrisation.

Contribution

Introduces a fast-wave slow-wave spectral deferred correction method for the Euler equations, achieving arbitrary order accuracy and good dispersion properties in weather prediction models.

Findings

Achieves high temporal and spatial accuracy in test cases

Demonstrates robustness in idealised weather prediction benchmarks

Successfully extends to include physics parametrisation with moisture and thermal effects

Abstract

This paper investigates the application of a fast-wave slow-wave spectral deferred correction time-stepping method (FWSW-SDC) to the compressible Euler equations. The resulting model achieves arbitrary order accuracy in time, demonstrating robust performance in standard benchmark idealised test cases for dynamical cores used for numerical weather prediction. The model uses a compatible finite element spatial discretisation, achieving good linear wave dispersion properties without spurious computational modes. A convergence test confirms the model's high temporal accuracy. Arbitrarily high spatial-temporal convergence is demonstrated using a gravity wave test case. The model is further extended to include the parametrisation of a simple physics process by adding two phases of moisture and its validity is demonstrated for a rising thermal problem. Finally, a baroclinic wave in simulated in a Cartesian domain.