Adaptively Implicit Advection for Atmospheric Flows
<|reference_start|>Adaptively Implicit Advection for Atmospheric Flows: Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit advection scheme facilitates efficient and robust integrations with long time-steps while having negligible impact on the overall accuracy, and achieving monotonicity and local conservation on general meshes. A novel and important aspect for the efficiency of the approach is that only one linear solver iteration is needed for each advection solve.   The implementation in this paper uses a second-order Runge-Kutta implicit/explicit time-stepping in combination with a second/third-order finite volume spatial discretisation. We demonstrate the adaptively implicit advection in the context of deformational flow advection on the sphere and a fully compressible model for atmospheric flows. Tracers are advected over the poles of latitude-longitude grids with very large Courant numbers and through hexagonal and cubed-sphere meshes with the same algorithm. Buoyant flow simulations with strong local updrafts also benefit from adaptively implicit advection. Stably stratified flow simulations require a stable combination of implicit treatment of gravity and acoustic waves as well as advection in order to achieve long stable time-steps.<|reference_end|>
@article{weller2024adaptively,
    title={Adaptively Implicit Advection for Atmospheric Flows},
    author={Hilary Weller, Christian Kuehnlein and Piotr K. Smolarkiewicz},
    journal={arXiv preprint arXiv:2406.08640},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.08640},
    primaryClass={physics.flu-dyn cs.NA math.NA}
}