TY - JOUR
T1 - A Review of Element-Based Galerkin Methods for Numerical Weather Prediction. Finite Elements, Spectral Elements, and Discontinuous Galerkin
AU - Marras, Simone
AU - Kelly, James
AU - Moragues Ginard, Margarida
AU - Mueller, Andreas
AU - Kopera, Michal A.
AU - Vasquez, Mariano
AU - Giraldo, Francis X.
AU - Houzeaux, Guillaume
AU - Jorba, Oriol
PY - 2015/5/15
Y1 - 2015/5/15
N2 - 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.
AB - 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.
KW - Discontinuous Galerkin
KW - Finite elements
KW - Galerkin methods
KW - HPC
KW - Numerical Weather Prediction
KW - Spectral Elements
KW - Stabilization.
UR - https://www.researchgate.net/publication/274313551_A_Review_of_Element-Based_Galerkin_Methods_for_Numerical_Weather_Prediction_Finite_Elements_Spectral_Elements_and_Discontinuous_Galerkin
U2 - 10.1007/s11831-015-9152-1
DO - 10.1007/s11831-015-9152-1
M3 - Article
VL - 23
JO - Archives of Computational Methods in Engineering
JF - Archives of Computational Methods in Engineering
IS - 4
ER -