Entropy and energy conservation for thermal atmospheric dynamics using mixed compatible finite elements

DOI10.1016/j.jcp.2023.112605arXiv2305.12343MaRDI QIDQ6117705

No author found.

Publication date: 21 February 2024

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.12343

zbMATH Keywords

energy conservationcompressible Euler equationsentropy conservationcompatible finite elementsthermal shallow water equationsthermal atmospheric dynamics

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Geophysics (86Axx)

Cites Work

• High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
• A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations
• A well-balanced central-upwind scheme for the thermal rotating shallow water equations
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• On discretely entropy conservative and entropy stable discontinuous Galerkin methods
• Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
• A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere
• An energetically balanced, quasi-Newton integrator for non-hydrostatic vertical atmospheric dynamics
• Exact spatial and temporal balance of energy exchanges within a horizontally explicit/vertically implicit non-hydrostatic atmosphere
• Entropy stable discontinuous Galerkin methods for balance laws in non-conservative form: applications to the Euler equations with gravity
• A quasi-Hamiltonian discretization of the thermal shallow water equations
• A mixed mimetic spectral element model of the 3D compressible Euler equations on the cubed sphere
• Energy-enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions
• Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
• Finite element exterior calculus, homological techniques, and applications
• The quasi-geostrophic theory of the thermal shallow water equations
• Compatible finite element methods for geophysical fluid dynamics