Steady states and well-balanced schemes for shallow water moment equations with topography

DOI10.1016/j.amc.2022.127166OpenAlexW3101256420MaRDI QIDQ2141230

Julian Koellermeier, Ernesto Pimentel-García

Publication date: 23 May 2022

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

Full work available at URL: https://arxiv.org/abs/2011.07667

zbMATH Keywords

shallow water equationssteady stateswell-balancedhyperbolic moment equations

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Incompressible inviscid fluids (76Bxx)

Uses Software

• PVM

Cites Work

• Unnamed Item
• High order exactly well-balanced numerical methods for shallow water systems
• A well-balanced reconstruction of wet/dry fronts for the shallow water equations
• The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems
• A weak formulation of Roe's approximate Riemann solver
• Upwind methods for hyperbolic conservation laws with source terms
• Numerical solution of hyperbolic moment models for the Boltzmann equation
• Semi-implicit finite difference methods for the two-dimensional shallow water equations
• A family of stable numerical solvers for the shallow water equations with source terms.
• Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems
• High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws
• Well-balanced high-order finite volume methods for systems of balance laws
• The Riemann problem for the shallow water equations with discontinuous topography: the wet-dry case
• Globally hyperbolic regularization of Grad's moment system in one dimensional space
• On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas
• The Riemann problem for the shallow water equations with discontinuous topography
• Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry
• Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
• The Riemann problem for the one-dimensional, free-surface shallow water equations with a bed step: theoretical analysis and numerical simulations
• A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies
• Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit
• Well-Balanced Schemes and Path-Conservative Numerical Methods
• A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods
• High order well balanced schemes for systems of balance laws
• On Well‐Balanced Finite Volume Methods for Nonconservative Nonhomogeneous Hyperbolic Systems
• Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws
• Central WENO schemes for hyperbolic systems of conservation laws
• A semi-implicit finite difference method for non-hydrostatic, free-surface flows
• Total variation diminishing Runge-Kutta schemes
• Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
• 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
• Moment Approximations and Model Cascades for Shallow Flow
• Analysis and Numerical Simulation of Hyperbolic Shallow Water Moment Equations
• Shallow Water Moment Models for Bedload Transport Problems
• On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems
• Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
• NUMERICAL TREATMENT OF WET/DRY FRONTS IN SHALLOW FLOWS WITH A MODIFIED ROE SCHEME
• Towards the ultimate conservative difference scheme I. The quest of monotonicity
• Exact solutions to the Riemann problem of the shallow water equations with a bottom step

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