A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying

DOI10.1002/fld.1674zbMath1142.76036OpenAlexW2120826174MaRDI QIDQ3522240

Serge Piperno, K. Djadel, Alexandre Ern

Publication date: 1 September 2008

Published in: International Journal for Numerical Methods in Fluids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/fld.1674

zbMATH Keywords

source termsflux modification techniqueslope modification technique

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Finite element methods applied to problems in fluid mechanics (76M10) Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing (76B10)

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Cites Work

• Unnamed Item
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• Flooding and drying in discontinuous Galerkin finite element discretizations of shallow-water equations. I: One dimension
• A discontinuous Galerkin method for three-dimensional shallow water equations
• A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations
• Space-time discontinuous Galerkin finite element method for shallow water flows
• On Godunov-type methods near low densities
• Weighted essentially non-oscillatory schemes
• Upwind methods for hyperbolic conservation laws with source terms
• Towards the ultimate conservative difference scheme. II: Monotonicity and conservation combined in a second-order scheme
• Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws.
• Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations.
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
• The resolution of the identity for selfadjoint Toeplitz operators with rational matrix symbol
• Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
• A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations
• An adaptive discretization of shallow-water equations based on discontinuous Galerkin methods
• Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
• On Godunov-Type Methods for Gas Dynamics
• Some exact solutions to the nonlinear shallow-water wave equations
• A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations
• Convergence of Second-Order Schemes for Isentropic Gas Dynamics
• A numerical model for the flooding and drying of irregular domains
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
• Zero mass error using unsteady wetting–drying conditions in shallow flows over dry irregular topography
• A split‐characteristic based finite element model for the shallow water equations
• The discontinuous Galerkin finite element method for the 2D shallow water equations