A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals

DOI10.1515/caim-2016-0026zbMath1398.86004OpenAlexW2564211620MaRDI QIDQ325748

Giovanni Tumolo

Publication date: 11 October 2016

Published in: Communications in Applied and Industrial Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/caim-2016-0026

zbMATH Keywords

shallow water equationsdiscontinuous Galerkin methodsqudrilateral meshessemi-implicit discretizationssemi-Lagrangian discretizations

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) 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) Computational methods for problems pertaining to geophysics (86-08)

Related Items (2)

Dynamical \(p\)-adaptivity for LES of compressible flows in a high order DG framework ⋮ The TR-BDF2 method for second order problems in structural mechanics

Uses Software

• TR-BDF2
• chammp

Cites Work

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• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• A standard test set for numerical approximations to the shallow water equations in spherical geometry
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• The Lagrange-Galerkin spectral element method on unstructured quadrilateral grids
• Stability, accuracy and efficiency of a semi-implicit method for three- dimensional shallow water flow
• Exact projections and the Lagrange-Galerkin method: A realistic alternative to quadrature
• A generalized particle search-locate algorithm for arbitrary grids
• Semi-implicit finite difference methods for the two-dimensional shallow water equations
• Finite elements and characteristics applied to advection-diffusion equations
• Evolution-Galerkin methods and their supraconvergence
• Analysis and implementation of TR-BDF2
• A semi-implicit, semi-Lagrangian, \(p\)-adaptive discontinuous Galerkin method for the shallow water equations
• Spurious inertial oscillations in shallow-water models
• Some conservation issues for the dynamical cores of NWP and climate models
• A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows
• Unsteady analytical solutions of the spherical shallow water equations
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• A Conservative Discontinuous Galerkin Semi-Implicit Formulation for the Navier–Stokes Equations in Nonhydrostatic Mesoscale Modeling
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Stability of the Lagrange-Galerkin method with non-exact integration
• On the Analysis of Finite Volume Methods for Evolutionary Problems
• Stability/dispersion analysis of the discontinuous Galerkin linearized shallow-water system
• Spectral/hp Element Methods for Computational Fluid Dynamics
• A semi-Lagrangian high-order method for Navier-Stokes equations

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