Artificial boundary layers in discontinuous Galerkin solutions to shallow water equations in channels

DOI10.1016/j.jcp.2015.07.015zbMath1351.76085OpenAlexW2175221335MaRDI QIDQ729276

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

Publication date: 20 December 2016

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2015.07.015

zbMATH Keywords

finite elementsshallow water equationsopen channeldiscontinuous Galerkiniso- and super-parametric finite elementsno-normal flow boundary conditionnumerical fluxes

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) 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)

Related Items

Foundations of the blended isogeometric discontinuous Galerkin (BIDG) method, Discontinuous Galerkin methods with nodal and hybrid modal/nodal triangular, quadrilateral, and polygonal elements for nonlinear shallow water flow, High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration, High-order discontinuous Galerkin methods for coastal hydrodynamics applications, Discontinuous Galerkin methods for plasma physics in the scrape-off layer of tokamaks, Performance comparison of HPX versus traditional parallelization strategies for the discontinuous Galerkin method

Uses Software

• ADCIRC
• TELEMAC

Cites Work

• Unnamed Item
• Discontinuous Galerkin methods with nodal and hybrid modal/nodal triangular, quadrilateral, and polygonal elements for nonlinear shallow water flow
• A performance comparison of continuous and discontinuous finite element shallow water models
• Implementation of a discontinuous Galerkin morphological model on two-dimensional unstructured meshes
• A fully implicit wetting-drying method for DG-FEM shallow water models, with an application to the scheldt estuary
• A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations
• Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations
• Semi discrete discontinuous Galerkin methods and stage-exceeding-order, strong-stability-preserving Runge-Kutta time discretizations
• A wave equation model for finite element tidal computations
• Spectral methods on triangles and other domains
• Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
• High-order accurate discontinuous finite element solution of the 2D Euler equations
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Hp discontinuous Galerkin methods for advection dominated problems in shallow water flow
• High-order accurate implementation of solid wall boundary conditions in curved geometries
• A discontinuous Galerkin finite element model for river bed evolution under shallow flows
• Strong Stability-Preserving High-Order Time Discretization Methods
• A performance comparison of nodal discontinuous Galerkin methods on triangles and quadrilaterals
• Partial Differential Equations and the Finite Element Method
• High degree efficient symmetrical Gaussian quadrature rules for the triangle
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Discontinuous Galerkin methods
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
• Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
• A high‐order triangular discontinuous Galerkin oceanic shallow water model
• Continuous, discontinuous and coupled discontinuous–continuous Galerkin finite element methods for the shallow water equations