A Review of Element-Based Galerkin Methods for Numerical Weather Prediction. Finite Elements, Spectral Elements, and Discontinuous Galerkin

Simone Marras, James Kelly, Margarida Moragues Ginard, Andreas Mueller, Michal A. Kopera, Mariano Vasquez, Francis X. Giraldo, Guillaume Houzeaux, Oriol Jorba

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

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.
Original languageAmerican English
JournalArchives of Computational Methods in Engineering
Volume23
Issue number4
DOIs
StatePublished - 15 May 2015

Keywords

  • Discontinuous Galerkin
  • Finite elements
  • Galerkin methods
  • HPC
  • Numerical Weather Prediction
  • Spectral Elements
  • Stabilization.

EGS Disciplines

  • Applied Mathematics
  • Numerical Analysis and Computation
  • Atmospheric Sciences

Fingerprint

Dive into the research topics of 'A Review of Element-Based Galerkin Methods for Numerical Weather Prediction. Finite Elements, Spectral Elements, and Discontinuous Galerkin'. Together they form a unique fingerprint.

Cite this