Numerical Analyses Of Exponential Time-Differencing Schemes For The Solution Of Atmospheric Models

In high-resolution numerical weather prediction models, fast-moving acoustic waves must be treated in a stable manner. Among the implicit-explicit (IMEX) schemes used for the solution of these models, horizontally explicit, vertically implicit (HEVI) methods show good stability and scalability on massively parallel machines. In this work, we present two classes of exponential time-differencing (ETD) methods for atmospheric models that use a HEVI splitting strategy, one being a three-stage method with the addition of artificial diffusion, the second based on a Strang splitting approach. The stability properties of the methods are analyzed and numerical examples are provided, which compare time-step restrictions and cost-to-accuracy ratios of the new methods with those for existing approaches.