Articles | Volume 9, issue 5
https://doi.org/10.5194/gmd-9-2007-2016
© Author(s) 2016. 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-9-2007-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Development and technical paper
| 
01 Jun 2016
Development and technical paper |
| 01 Jun 2016
A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models
Jorge E. Guerra
CORRESPONDING AUTHOR
Department of Land, Air and Water Resources, University of California, Davis, One Shields Ave., Davis, CA 95616, USA
Paul A. Ullrich
Department of Land, Air and Water Resources, University of California, Davis, One Shields Ave., Davis, CA 95616, USA
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Cited
30 citations as recorded by crossref.
- Vertical Discretization for a Nonhydrostatic Atmospheric Model Based on High-Order Spectral Elements T. Yi & F. Giraldo https://doi.org/10.1175/MWR-D-18-0283.1
- 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
- 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
- A mixed finite‐element, finite‐volume, semi‐implicit discretization for atmospheric dynamics: Cartesian geometry T. Melvin et al. https://doi.org/10.1002/qj.3501
- An Assessment of Nonhydrostatic and Hydrostatic Dynamical Cores at Seasonal Time Scales in the Energy Exascale Earth System Model (E3SM) W. Liu et al. https://doi.org/10.1029/2021MS002805
- An entropy conserving/stable discontinuous Galerkin solver in entropy variables based on the direct enforcement of entropy balance L. Alberti et al. https://doi.org/10.1016/j.jcp.2024.113007
- The hectometric modelling challenge: Gaps in the current state of the art and ways forward towards the implementation of 100‐m scale weather and climate models H. Lean et al. https://doi.org/10.1002/qj.4858
- 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
- Evaluation of Implicit‐Explicit Additive Runge‐Kutta Integrators for the HOMME‐NH Dynamical Core C. Vogl et al. https://doi.org/10.1029/2019MS001700
- The DOE E3SM Model Version 2: Overview of the Physical Model and Initial Model Evaluation J. Golaz et al. https://doi.org/10.1029/2022MS003156
- 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
- A compatible finite element discretisation for the nonhydrostatic vertical slice equations C. Cotter & J. Shipton https://doi.org/10.1007/s13137-023-00236-7
- A performance study of horizontally explicit vertically implicit (HEVI) time-integrators for non-hydrostatic atmospheric models F. Giraldo et al. https://doi.org/10.1016/j.jcp.2024.113275
- An energy consistent summation-by-parts finite difference discretization for the non-hydrostatic atmospheric dynamics equations on the cubed-sphere grid D. Markhanov et al. https://doi.org/10.1515/rnam-2025-0010
- Quantifying and attributing time step sensitivities in present-day climate simulations conducted with EAMv1 H. Wan et al. https://doi.org/10.5194/gmd-14-1921-2021
- A Global Nonhydrostatic Atmospheric Model with a Mass- and Energy-conserving Vertically Implicit Correction (VIC) Scheme H. Ge 葛華 et al. https://doi.org/10.3847/1538-4357/ab9ec7
- 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
- An Idealized Test of the Response of the Community Atmosphere Model to Near‐Grid‐Scale Forcing Across Hydrostatic Resolutions A. Herrington & K. Reed https://doi.org/10.1002/2017MS001078
- Simulating Nonhydrostatic Atmospheres on Planets (SNAP): Formulation, Validation, and Application to the Jovian Atmosphere C. Li & X. Chen https://doi.org/10.3847/1538-4365/aafdaa
- A family of well-balanced WENO and TENO schemes for atmospheric flows A. Navas-Montilla & I. Echeverribar https://doi.org/10.1016/j.jcp.2023.112273
- Difference in boreal winter predictability between two dynamical cores of Community Atmosphere Model 5 H. Kim et al. https://doi.org/10.1088/1748-9326/ad0fbf
- An Energy Consistent Discretization of the Nonhydrostatic Equations in Primitive Variables M. Taylor et al. https://doi.org/10.1029/2019MS001783
- Exploring the potential of TENO and WENO schemes for simulating under-resolved turbulent flows in the atmosphere using Euler equations A. Navas-Montilla et al. https://doi.org/10.1016/j.compfluid.2024.106349
- Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models D. Gardner et al. https://doi.org/10.5194/gmd-11-1497-2018
- Finite Elements Used in the Vertical Discretization of the Fully Compressible Core of the ALADIN System J. Vivoda et al. https://doi.org/10.1175/MWR-D-18-0043.1
- Understanding the dependence of storm splitting on numerical models: Comparing UM and WRF A. Dipankar et al. https://doi.org/10.1002/qj.4025
- Removing Numerical Pathologies in a Turbulence Parameterization Through Convergence Testing S. Zhang et al. https://doi.org/10.1029/2023MS003633
- Zooming in: SCREAM at 100 m using regional refinement over the San Francisco Bay Area J. Zhang et al. https://doi.org/10.5194/gmd-19-795-2026
- Choice of function spaces for thermodynamic variables in mixed finite‐element methods T. Melvin et al. https://doi.org/10.1002/qj.3268
- An Objective and Efficient Method for Assessing the Impact of Reduced‐Precision Calculations On Solution Correctness S. Zhang et al. https://doi.org/10.1029/2019MS001817
30 citations as recorded by crossref.
- Vertical Discretization for a Nonhydrostatic Atmospheric Model Based on High-Order Spectral Elements T. Yi & F. Giraldo https://doi.org/10.1175/MWR-D-18-0283.1
- 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
- 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
- A mixed finite‐element, finite‐volume, semi‐implicit discretization for atmospheric dynamics: Cartesian geometry T. Melvin et al. https://doi.org/10.1002/qj.3501
- An Assessment of Nonhydrostatic and Hydrostatic Dynamical Cores at Seasonal Time Scales in the Energy Exascale Earth System Model (E3SM) W. Liu et al. https://doi.org/10.1029/2021MS002805
- An entropy conserving/stable discontinuous Galerkin solver in entropy variables based on the direct enforcement of entropy balance L. Alberti et al. https://doi.org/10.1016/j.jcp.2024.113007
- The hectometric modelling challenge: Gaps in the current state of the art and ways forward towards the implementation of 100‐m scale weather and climate models H. Lean et al. https://doi.org/10.1002/qj.4858
- 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
- Evaluation of Implicit‐Explicit Additive Runge‐Kutta Integrators for the HOMME‐NH Dynamical Core C. Vogl et al. https://doi.org/10.1029/2019MS001700
- The DOE E3SM Model Version 2: Overview of the Physical Model and Initial Model Evaluation J. Golaz et al. https://doi.org/10.1029/2022MS003156
- 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
- A compatible finite element discretisation for the nonhydrostatic vertical slice equations C. Cotter & J. Shipton https://doi.org/10.1007/s13137-023-00236-7
- A performance study of horizontally explicit vertically implicit (HEVI) time-integrators for non-hydrostatic atmospheric models F. Giraldo et al. https://doi.org/10.1016/j.jcp.2024.113275
- An energy consistent summation-by-parts finite difference discretization for the non-hydrostatic atmospheric dynamics equations on the cubed-sphere grid D. Markhanov et al. https://doi.org/10.1515/rnam-2025-0010
- Quantifying and attributing time step sensitivities in present-day climate simulations conducted with EAMv1 H. Wan et al. https://doi.org/10.5194/gmd-14-1921-2021
- A Global Nonhydrostatic Atmospheric Model with a Mass- and Energy-conserving Vertically Implicit Correction (VIC) Scheme H. Ge 葛華 et al. https://doi.org/10.3847/1538-4357/ab9ec7
- 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
- An Idealized Test of the Response of the Community Atmosphere Model to Near‐Grid‐Scale Forcing Across Hydrostatic Resolutions A. Herrington & K. Reed https://doi.org/10.1002/2017MS001078
- Simulating Nonhydrostatic Atmospheres on Planets (SNAP): Formulation, Validation, and Application to the Jovian Atmosphere C. Li & X. Chen https://doi.org/10.3847/1538-4365/aafdaa
- A family of well-balanced WENO and TENO schemes for atmospheric flows A. Navas-Montilla & I. Echeverribar https://doi.org/10.1016/j.jcp.2023.112273
- Difference in boreal winter predictability between two dynamical cores of Community Atmosphere Model 5 H. Kim et al. https://doi.org/10.1088/1748-9326/ad0fbf
- An Energy Consistent Discretization of the Nonhydrostatic Equations in Primitive Variables M. Taylor et al. https://doi.org/10.1029/2019MS001783
- Exploring the potential of TENO and WENO schemes for simulating under-resolved turbulent flows in the atmosphere using Euler equations A. Navas-Montilla et al. https://doi.org/10.1016/j.compfluid.2024.106349
- Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models D. Gardner et al. https://doi.org/10.5194/gmd-11-1497-2018
- Finite Elements Used in the Vertical Discretization of the Fully Compressible Core of the ALADIN System J. Vivoda et al. https://doi.org/10.1175/MWR-D-18-0043.1
- Understanding the dependence of storm splitting on numerical models: Comparing UM and WRF A. Dipankar et al. https://doi.org/10.1002/qj.4025
- Removing Numerical Pathologies in a Turbulence Parameterization Through Convergence Testing S. Zhang et al. https://doi.org/10.1029/2023MS003633
- Zooming in: SCREAM at 100 m using regional refinement over the San Francisco Bay Area J. Zhang et al. https://doi.org/10.5194/gmd-19-795-2026
- Choice of function spaces for thermodynamic variables in mixed finite‐element methods T. Melvin et al. https://doi.org/10.1002/qj.3268
- An Objective and Efficient Method for Assessing the Impact of Reduced‐Precision Calculations On Solution Correctness S. Zhang et al. https://doi.org/10.1029/2019MS001817
Saved (final revised paper)
Latest update: 03 Jun 2026
Short summary
This work introduces a collection of advances in the field of numerical simulation of the atmosphere using mixed finite element methods. We emphasize vertical motions in the atmosphere and apply state-of-the-art mathematics and programming paradigms to solve the differential equations that govern air flow cast in a coordinate-free formulation. The simulations show accurate flow features over a wide range of spatial scales including several important phenomena.
This work introduces a collection of advances in the field of numerical simulation of the...
