High-order discontinuous Galerkin methods for coastal hydrodynamics applications

DOI10.1016/j.cma.2019.07.003zbMath1441.76054OpenAlexW2962429517MaRDI QIDQ1988254

S. R. Brus, Ethan J. Kubatko, Joannes J. Westerink, Damrongsak Wirasaet, Clint N. Dawson

Publication date: 16 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2019.07.003

zbMATH Keywords

finite element methodshallow water equationsparallel computingdiscontinuous Galerkinhigh-order numerical methodscoastal hydrodynamics

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) 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) Waves for incompressible viscous fluids (76D33)

Related Items (3)

A high-order velocity-based discontinuous Galerkin scheme for the shallow water equations: local conservation, entropy stability, well-balanced property, and positivity preservation ⋮ A curved boundary treatment for discontinuous Galerkin method applied to Euler equations on triangular and tetrahedral grids ⋮ High-order compact gas-kinetic scheme for two-layer shallow water equations on unstructured mesh

Uses Software

• Gmsh
• ADCIRC
• GEOCLAW
• DistMesh
• TELEMAC

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Robust untangling of curvilinear meshes
• Discontinuous Galerkin methods with nodal and hybrid modal/nodal triangular, quadrilateral, and polygonal elements for nonlinear shallow water flow
• Performance and scalability improvements for discontinuous Galerkin solutions to conservation laws on unstructured grids
• A performance comparison of continuous and discontinuous finite element shallow water models
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• Artificial boundary layers in discontinuous Galerkin solutions to shallow water equations in channels
• High-order unstructured curved mesh generation using the Winslow equations
• Propagation of error into regions of smoothness for non-linear approximations to hyperbolic equations
• Some tests of precision for a finite element model of ocean tides
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• Spectral methods on triangles and other domains
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Parallel, adaptive finite element methods for conservation laws
• High-order accurate discontinuous finite element solution of the 2D Euler equations
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
• Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes
• Hp discontinuous Galerkin methods for advection dominated problems in shallow water flow
• Strong Stability-Preserving High-Order Time Discretization Methods
• Tsunami modelling with adaptively refined finite volume methods
• A triangular spectral/hp discontinuous Galerkin method for modelling 2D 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
• Boundary discretization for high-order discontinuous Galerkin computations of tidal flows around shallow water islands
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• High degree efficient symmetrical Gaussian quadrature rules for the triangle
• An Optimal-Order Error Estimate for the Discontinuous Galerkin Method
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Surfaces Generated by Moving Least Squares Methods
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Mesh generation in curvilinear domains using high‐order elements
• From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex
• A Simple Mesh Generator in MATLAB
• High‐order CFD methods: current status and perspective
• A high‐order triangular discontinuous Galerkin oceanic shallow water model
• The discontinuous Galerkin finite element method for the 2D shallow water equations

This page was built for publication: High-order discontinuous Galerkin methods for coastal hydrodynamics applications