Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations

DOI10.1016/j.jcp.2019.109016zbMath1453.65438arXiv1901.06349OpenAlexW2909028901WikidataQ127085431 ScholiaQ127085431MaRDI QIDQ2222700

Golo A. Wimmer, Werner Bauer, Colin John Cotter

Publication date: 27 January 2021

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

Full work available at URL: https://arxiv.org/abs/1901.06349

zbMATH Keywords

shallow water equationsHamiltonian mechanicsupwindingcompatible finite element methods

Mathematics Subject Classification ID

Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Meteorology and atmospheric physics (86A10) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (10)

An energetically balanced, quasi-Newton integrator for non-hydrostatic vertical atmospheric dynamics ⋮ Computational Modeling for High-Fidelity Coarsening of Shallow Water Equations Based on Subgrid Data ⋮ A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere ⋮ Compatible finite element methods for geophysical fluid dynamics ⋮ A compatible finite element discretisation for the nonhydrostatic vertical slice equations ⋮ SUPG formulation augmented with YZβ shock‐capturing for computing shallow‐water equations ⋮ Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics ⋮ Petrov-Galerkin flux upwinding for mixed mimetic spectral elements, and its application to geophysical flow problems ⋮ Energy conserving SUPG methods for compatible finite element schemes in numerical weather prediction ⋮ Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation

Uses Software

• chammp
• Firedrake
• TSFC
• COFFEE
• Slate

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Linear energy-preserving integrators for Poisson systems
• Residual distribution schemes: current status and future trends
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• A standard test set for numerical approximations to the shallow water equations in spherical geometry
• A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere
• Higher-order compatible finite element schemes for the nonlinear rotating shallow water equations on the sphere
• A quasi-Hamiltonian discretization of the thermal shallow water equations
• Energy-enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions
• Mixed finite elements for numerical weather prediction
• Hamiltonian description of the ideal fluid
• An Algorithm for the Optimization of Finite Element Integration Loops
• Firedrake
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A variational $\boldsymbol{H}({\rm div})$ finite-element discretization approach for perfect incompressible fluids
• TSFC: A Structure-Preserving Form Compiler

This page was built for publication: Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations