Article
A Review of Element-Based Galerkin Methods for Numerical Weather Prediction. Finite Elements, Spectral Elements, and Discontinuous Galerkin
Archives of Computational Methods in Engineering
(2015)
Abstract
Numerical Weather Prediction (NWP) is in a period of transition. As resolutions increase, global models are moving towards fully nonhydrostatic dynamical cores, with the local and global models using the same governing equations; therefore we have reached a point where it may be possible to use a single model for both applications. These new dynamical cores are designed to scale efficiently on clusters with hundreds of thousands or even millions of CPU cores and GPUs. Operational and research NWP codes currently use a wide range of numerical methods: finite difference, spectral transform, finite volume and, increasingly, finite/spectral elements and discontinuous Galerkin, which constitute element-based Galerkin (EBG) methods. Due to their important role in this transition, will EBGs be the dominant power behind NWP in the next 10 years, or will they just be one of many methods to chose from? One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (2003) [{\it Review of numerical methods for nonhydrostatic weather prediction models} Meteorol. Atmos. Phys. 82, 2003], this review discusses EBG methods as a viable numerical approach for the next-generation NWP models. One well-known weakness of EBG methods is the generation of unphysical oscillations in advection-dominated flows; special attention is hence devoted to dissipation-based stabilization methods. % such as, but not limited to, variational multi-scale stabilization (VMS) or dynamic Large Eddy Simulation (LES) used for stabilization. Since EBGs are geometrically flexible and allow both conforming and non-conforming meshes, as well as grid adaptivity, this review is concluded with a short overview of how mesh generation and dynamic mesh refinement are becoming as important for atmospheric modeling as they have been for engineering applications for many years.
Keywords
- Galerkin methods,
- Finite elements,
- Spectral Elements,
- Discontinuous Galerkin,
- HPC,
- Stabilization.,
- Numerical Weather Prediction
Disciplines
Publication Date
May 15, 2015
DOI
10.1007/s11831-015-9152-1
Citation Information
Simone Marras, James Kelly, Margarida Moragues Ginard, Andreas Mueller, et al.. "A Review of Element-Based Galerkin Methods for Numerical Weather Prediction. Finite Elements, Spectral Elements, and Discontinuous Galerkin" Archives of Computational Methods in Engineering Vol. 23 Iss. 4 (2015) p. 673 - 722 Available at: http://works.bepress.com/michal-kopera/8/