Articles | Volume 10, issue 2
https://doi.org/10.5194/gmd-10-791-2017
© Author(s) 2017. 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-10-791-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Development and technical paper
| 
17 Feb 2017
Development and technical paper |
| 17 Feb 2017
Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods – Part 1: Derivation and properties
Christopher Eldred
CORRESPONDING AUTHOR
LAGA, University of Paris 13, Villetaneuse, France
David Randall
Department of Atmospheric Science, Colorado State University, Fort Collins, USA
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Cited
20 citations as recorded by crossref.
- Energy–enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions W. Bauer & C. Cotter https://doi.org/10.1016/j.jcp.2018.06.071
- A Total Energy Error Analysis of Dynamical Cores and Physics‐Dynamics Coupling in the Community Atmosphere Model (CAM) P. Lauritzen & D. Williamson https://doi.org/10.1029/2018MS001549
- Generalized Z-Grid Model for Numerical Weather Prediction Y. Xie https://doi.org/10.3390/atmos10040179
- Summation-by-parts finite-difference shallow water model on the cubed-sphere grid. Part I: Non-staggered grid V. Shashkin et al. https://doi.org/10.1016/j.jcp.2022.111797
- Discretization of generalized Coriolis and friction terms on the deformed hexagonal C‐grid A. Gassmann https://doi.org/10.1002/qj.3294
- Discrete conservation properties for shallow water flows using mixed mimetic spectral elements D. Lee et al. https://doi.org/10.1016/j.jcp.2017.12.022
- A hybrid discrete exterior calculus and finite difference method for Boussinesq convection in spherical shells B. Mantravadi et al. https://doi.org/10.1016/j.jcp.2023.112397
- A conservative numerical scheme for the multilayer shallow‐water equations on unstructured meshes Q. Chen https://doi.org/10.1002/qj.4994
- On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet B. Shashikanth https://doi.org/10.1016/j.physd.2025.134978
- A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere D. Lee & A. Palha https://doi.org/10.1016/j.jcp.2018.08.042
- A quasi-Hamiltonian discretization of the thermal shallow water equations C. Eldred et al. https://doi.org/10.1016/j.jcp.2018.10.038
- Conservative numerical schemes with optimal dispersive wave relations: Part I. Derivation and analysis Q. Chen et al. https://doi.org/10.1007/s00211-021-01218-3
- Investigating Inherent Numerical Stabilization for the Moist, Compressible, Non‐Hydrostatic Euler Equations on Collocated Grids M. Norman et al. https://doi.org/10.1029/2023MS003732
- Challenges in Developing Finite-Volume Global Weather and Climate Models with Focus on Numerical Accuracy Y. Xie & Z. Qin https://doi.org/10.1007/s13351-021-0202-3
- A center compact scheme for the Shallow Water equations on the sphere M. Brachet & J. Croisille https://doi.org/10.1016/j.compfluid.2021.105286
- Variational integrator for the rotating shallow‐water equations on the sphere R. Brecht et al. https://doi.org/10.1002/qj.3477
- A consistent mass-conserving C-staggered method for shallow water equations on global reduced grids G. Lima & P. Peixoto https://doi.org/10.1016/j.jcp.2022.111741
- Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods – Part 1: Derivation and properties C. Eldred & D. Randall https://doi.org/10.5194/gmd-10-791-2017
- Surprisingly tight Courant–Friedrichs–Lewy condition in explicit high-order Arakawa schemes M. Raeth & K. Hallatschek https://doi.org/10.1063/5.0223009
- Reconciling and Improving Formulations for Thermodynamics and Conservation Principles in Earth System Models (ESMs) P. Lauritzen et al. https://doi.org/10.1029/2022MS003117
20 citations as recorded by crossref.
- Energy–enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions W. Bauer & C. Cotter https://doi.org/10.1016/j.jcp.2018.06.071
- A Total Energy Error Analysis of Dynamical Cores and Physics‐Dynamics Coupling in the Community Atmosphere Model (CAM) P. Lauritzen & D. Williamson https://doi.org/10.1029/2018MS001549
- Generalized Z-Grid Model for Numerical Weather Prediction Y. Xie https://doi.org/10.3390/atmos10040179
- Summation-by-parts finite-difference shallow water model on the cubed-sphere grid. Part I: Non-staggered grid V. Shashkin et al. https://doi.org/10.1016/j.jcp.2022.111797
- Discretization of generalized Coriolis and friction terms on the deformed hexagonal C‐grid A. Gassmann https://doi.org/10.1002/qj.3294
- Discrete conservation properties for shallow water flows using mixed mimetic spectral elements D. Lee et al. https://doi.org/10.1016/j.jcp.2017.12.022
- A hybrid discrete exterior calculus and finite difference method for Boussinesq convection in spherical shells B. Mantravadi et al. https://doi.org/10.1016/j.jcp.2023.112397
- A conservative numerical scheme for the multilayer shallow‐water equations on unstructured meshes Q. Chen https://doi.org/10.1002/qj.4994
- On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet B. Shashikanth https://doi.org/10.1016/j.physd.2025.134978
- A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere D. Lee & A. Palha https://doi.org/10.1016/j.jcp.2018.08.042
- A quasi-Hamiltonian discretization of the thermal shallow water equations C. Eldred et al. https://doi.org/10.1016/j.jcp.2018.10.038
- Conservative numerical schemes with optimal dispersive wave relations: Part I. Derivation and analysis Q. Chen et al. https://doi.org/10.1007/s00211-021-01218-3
- Investigating Inherent Numerical Stabilization for the Moist, Compressible, Non‐Hydrostatic Euler Equations on Collocated Grids M. Norman et al. https://doi.org/10.1029/2023MS003732
- Challenges in Developing Finite-Volume Global Weather and Climate Models with Focus on Numerical Accuracy Y. Xie & Z. Qin https://doi.org/10.1007/s13351-021-0202-3
- A center compact scheme for the Shallow Water equations on the sphere M. Brachet & J. Croisille https://doi.org/10.1016/j.compfluid.2021.105286
- Variational integrator for the rotating shallow‐water equations on the sphere R. Brecht et al. https://doi.org/10.1002/qj.3477
- A consistent mass-conserving C-staggered method for shallow water equations on global reduced grids G. Lima & P. Peixoto https://doi.org/10.1016/j.jcp.2022.111741
- Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods – Part 1: Derivation and properties C. Eldred & D. Randall https://doi.org/10.5194/gmd-10-791-2017
- Surprisingly tight Courant–Friedrichs–Lewy condition in explicit high-order Arakawa schemes M. Raeth & K. Hallatschek https://doi.org/10.1063/5.0223009
- Reconciling and Improving Formulations for Thermodynamics and Conservation Principles in Earth System Models (ESMs) P. Lauritzen et al. https://doi.org/10.1029/2022MS003117
Saved (final revised paper)
Latest update: 01 Jun 2026
Short summary
This paper represents research done on improving our ability to make future predictions about weather and climate, through the use of computer models. Specifically, we are aiming to improve the ability of such simulations to represent fundamental physical processes such as conservation laws. We found that it was possible to obtain a computer model with better conservation properties by using a specific set of mathematical tools (called Hamiltonian methods).
This paper represents research done on improving our ability to make future predictions about...
