Articles | Volume 7, issue 6
https://doi.org/10.5194/gmd-7-3017-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/gmd-7-3017-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Development and technical paper
| 
17 Dec 2014
Development and technical paper |
| 17 Dec 2014
A global finite-element shallow-water model supporting continuous and discontinuous elements
Department of Land, Air and Water Resources, University of California, Davis, One Shields Ave., Davis, CA 95616, USA
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
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Cited
17 citations as recorded by crossref.
- DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models P. Ullrich et al. https://doi.org/10.5194/gmd-10-4477-2017
- Development of a high-order global dynamical core using the discontinuous Galerkin method for an atmospheric large-eddy simulation (LES) and proposal of test cases: SCALE-DG v0.8.0 Y. Kawai & H. Tomita https://doi.org/10.5194/gmd-18-725-2025
- Impact and importance of hyperdiffusion on the spectral element method: A linear dispersion analysis P. Ullrich et al. https://doi.org/10.1016/j.jcp.2018.06.035
- o3o3: A Variant of Spectral Elements with a Regular Collocation Grid J. Steppeler et al. https://doi.org/10.1175/MWR-D-18-0288.1
- High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid S. Gaudreault et al. https://doi.org/10.1016/j.jcp.2021.110792
- Multigrid preconditioners for the mixed finite element dynamical core of the LFRic atmospheric model C. Maynard et al. https://doi.org/10.1002/qj.3880
- Physics–Dynamics Coupling with Element-Based High-Order Galerkin Methods: Quasi-Equal-Area Physics Grid A. Herrington et al. https://doi.org/10.1175/MWR-D-18-0136.1
- A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models J. Guerra & P. Ullrich https://doi.org/10.5194/gmd-9-2007-2016
- A mixed finite-element discretisation of the shallow-water equations J. Kent et al. https://doi.org/10.5194/gmd-16-1265-2023
- The Matsuno baroclinic wave test case O. Shamir et al. https://doi.org/10.5194/gmd-12-2181-2019
- Applying of a Gridless Method in Data Assimilation System X. Yuan & X. Liang https://doi.org/10.1007/s13351-026-5048-2
- A marshalled data format for pointers in relocatable data blocks N. Vrvilo et al. https://doi.org/10.1145/3156685.3092276
- Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models D. Gardner et al. https://doi.org/10.5194/gmd-11-1497-2018
- NCAR Release of CAM‐SE in CESM2.0: A Reformulation of the Spectral Element Dynamical Core in Dry‐Mass Vertical Coordinates With Comprehensive Treatment of Condensates and Energy P. Lauritzen et al. https://doi.org/10.1029/2017MS001257
- Spectral steady-state solutions to the 2D compressible Euler equations for cross-mountain flows J. Guerra & P. Ullrich https://doi.org/10.2140/camcos.2021.16.99
- HelioCubed: A High Order Inner Heliosphere Simulation Code with a Mapped Cubed Sphere Grid and Adaptive Mesh Refinement T. Singh et al. https://doi.org/10.1088/1742-6596/2997/1/012019
- Two-Dimensional Evaluation of ATHAM-Fluidity, a Nonhydrostatic Atmospheric Model Using Mixed Continuous/Discontinuous Finite Elements and Anisotropic Grid Optimization J. Savre et al. https://doi.org/10.1175/MWR-D-15-0398.1
17 citations as recorded by crossref.
- DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models P. Ullrich et al. https://doi.org/10.5194/gmd-10-4477-2017
- Development of a high-order global dynamical core using the discontinuous Galerkin method for an atmospheric large-eddy simulation (LES) and proposal of test cases: SCALE-DG v0.8.0 Y. Kawai & H. Tomita https://doi.org/10.5194/gmd-18-725-2025
- Impact and importance of hyperdiffusion on the spectral element method: A linear dispersion analysis P. Ullrich et al. https://doi.org/10.1016/j.jcp.2018.06.035
- o3o3: A Variant of Spectral Elements with a Regular Collocation Grid J. Steppeler et al. https://doi.org/10.1175/MWR-D-18-0288.1
- High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid S. Gaudreault et al. https://doi.org/10.1016/j.jcp.2021.110792
- Multigrid preconditioners for the mixed finite element dynamical core of the LFRic atmospheric model C. Maynard et al. https://doi.org/10.1002/qj.3880
- Physics–Dynamics Coupling with Element-Based High-Order Galerkin Methods: Quasi-Equal-Area Physics Grid A. Herrington et al. https://doi.org/10.1175/MWR-D-18-0136.1
- A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models J. Guerra & P. Ullrich https://doi.org/10.5194/gmd-9-2007-2016
- A mixed finite-element discretisation of the shallow-water equations J. Kent et al. https://doi.org/10.5194/gmd-16-1265-2023
- The Matsuno baroclinic wave test case O. Shamir et al. https://doi.org/10.5194/gmd-12-2181-2019
- Applying of a Gridless Method in Data Assimilation System X. Yuan & X. Liang https://doi.org/10.1007/s13351-026-5048-2
- A marshalled data format for pointers in relocatable data blocks N. Vrvilo et al. https://doi.org/10.1145/3156685.3092276
- Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models D. Gardner et al. https://doi.org/10.5194/gmd-11-1497-2018
- NCAR Release of CAM‐SE in CESM2.0: A Reformulation of the Spectral Element Dynamical Core in Dry‐Mass Vertical Coordinates With Comprehensive Treatment of Condensates and Energy P. Lauritzen et al. https://doi.org/10.1029/2017MS001257
- Spectral steady-state solutions to the 2D compressible Euler equations for cross-mountain flows J. Guerra & P. Ullrich https://doi.org/10.2140/camcos.2021.16.99
- HelioCubed: A High Order Inner Heliosphere Simulation Code with a Mapped Cubed Sphere Grid and Adaptive Mesh Refinement T. Singh et al. https://doi.org/10.1088/1742-6596/2997/1/012019
- Two-Dimensional Evaluation of ATHAM-Fluidity, a Nonhydrostatic Atmospheric Model Using Mixed Continuous/Discontinuous Finite Elements and Anisotropic Grid Optimization J. Savre et al. https://doi.org/10.1175/MWR-D-15-0398.1
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Latest update: 29 Oct 2026
Short summary
This paper compares continuous and discontinuous discretizations of the shallow-water equations on the sphere using the flux reconstruction formulation. The discontinuous framework comes at a cost, including a reduced time step size and higher computational expense, but has a number of desirable properties which may make it desirable for future use in atmospheric models.
This paper compares continuous and discontinuous discretizations of the shallow-water equations...
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