WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE

DOI10.1142/S021820250700256XzbMath1137.76038MaRDI QIDQ3502921

Alberto Pardo Milanés, C. Parés-Madroñal, Manuel J. Castro

Publication date: 20 May 2008

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

finite volume methodRoe methodpath-conservative methodtwo-layer shallow water system

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite volume methods applied to problems in fluid mechanics (76M12)

Related Items

A well balanced diffuse interface method for complex nonhydrostatic free surface flows, A fully well-balanced scheme for the 1D blood flow equations with friction source term, Well-balanced finite volume schemes for nearly steady adiabatic flows, Well-balanced high-order finite difference methods for systems of balance laws, Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations, High order sign-preserving and well-balanced exponential Runge-Kutta discontinuous Galerkin methods for the shallow water equations with friction, FullSWOF Paral: Comparison of two parallelization strategies (MPI and SKELGIS) on a software designed for hydrology applications, Parallelization of a relaxation scheme modelling the bedload transport of sediments in shallow water flow, Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed, Recent advances on the discontinuous Galerkin method for shallow water equations with topography source terms, A finite volume method for numerical simulation of shallow water models with porosity, A shallow water with variable pressure model for blood flow simulation, An efficient splitting technique for two-layer shallow-water model, Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows, A Fully Well-Balanced Lagrange--Projection-Type Scheme for the Shallow-Water Equations, A well-balanced Runge-Kutta discontinuous Galerkin method for the Euler equations in isothermal hydrostatic state under gravitational field, High order exactly well-balanced numerical methods for shallow water systems, A well-balanced ADER discontinuous Galerkin method based on differential transformation procedure for shallow water equations, A multi well-balanced scheme for the shallow water MHD system with topography, Well-balanced numerical resolution of the two-layer shallow water equations under rigid-lid with wet-dry fronts, Well-balanced discontinuous Galerkin methods with hydrostatic reconstruction for the Euler equations with gravitation, A well-balanced scheme for the shallow-water equations with topography or Manning friction, Well balancing of the SWE schemes for moving-water steady flows, Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties, Unnamed Item, A Well-Balanced Scheme for Euler Equations with Singular Sources, The exact Riemann solver to the shallow water equations for natural channels with bottom steps, A Well-Balanced Partial Relaxation Scheme for the Two-Dimensional Saint-Venant System, High-order fully well-balanced numerical methods for one-dimensional blood flow with discontinuous properties, Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Scheme for the Thermal Rotating Shallow Water Equations, Flux globalization based well-balanced central-upwind schemes for hydrodynamic equations with general free energy, Path-conservative positivity-preserving well-balanced finite volume WENO method for porous shallow water equations, Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: global flux quadrature and cell entropy correction, 2D granular flows with the \(\mu(I)\) rheology and side walls friction: a well-balanced multilayer discretization, A geometrically intrinsic Lagrangian-Eulerian scheme for 2D shallow water equations with variable topography and discontinuous data, Efficient well-balanced hydrostatic upwind schemes for shallow-water equations, A limitation of the hydrostatic reconstruction technique for shallow water equations, Energy-stable staggered schemes for the shallow water equations, Reliability of first order numerical schemes for solving shallow water system over abrupt topography, Moving-Water Equilibria Preserving Partial Relaxation Scheme for the Saint-Venant System, Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes, A fully well-balanced and asymptotic preserving scheme for the shallow-water equations with a generalized Manning friction source term, Second-order well-balanced Lagrange-projection schemes for blood flow equations, Very high order well-balanced schemes for non-prismatic one-dimensional channels with arbitrary shape, Low-Shapiro hydrostatic reconstruction technique for blood flow simulation in large arteries with varying geometrical and mechanical properties, A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction, Capturing Near-Equilibrium Solutions: A Comparison between High-Order Discontinuous Galerkin Methods and Well-Balanced Schemes, A well-balanced scheme for the shallow-water equations with topography, On the well-balanced numerical discretization of shallow water equations on unstructured meshes, One-Dimensional Blood Flow with Discontinuous Properties and Transport: Mathematical Analysis and Numerical Schemes, Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system, On some fast well-balanced first order solvers for nonconservative systems, Numerical treatment of the loss of hyperbolicity of the two-layer shallow-water system, On an intermediate field capturing Riemann solver based on a parabolic viscosity matrix for the two-layer shallow water system, Shallow water flows in channels, On the convergence and well-balanced property of path-conservative numerical schemes for systems of balance laws, A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations, Asymptotic preserving scheme for the shallow water equations with source terms on unstructured meshes, A comparison between bottom-discontinuity numerical treatments in the DG framework, Positivity-preserving well-balanced arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the shallow water equations, Well-balanced high-order finite volume methods for systems of balance laws, An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density, Finite-volume schemes for shallow-water equations, The Riemann problem for the shallow water equations with discontinuous topography: the wet-dry case, Convergence of the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography, High-Order Well-Balanced Finite-Volume Schemes for Hydrodynamic Equations With Nonlocal Free Energy, Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws

Cites Work

• A multilayer Saint-Venant model: derivation and numerical validation
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Approximate Riemann solvers, parameter vectors, and difference schemes
• A weak formulation of Roe's approximate Riemann solver
• Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
• Upwind methods for hyperbolic conservation laws with source terms
• Asymptotically balanced schemes for non-homogeneous hyperbolic systems -- application to the shallow water equations.
• Numerical simulation of two-layer shallow water flows through channels with irregular geometry.
• Schéma nonlinéaire pour l'approximation numérique d'un système hyperbolique non conservatif. (Nonlinear scheme to approximate nonconservative hyperbolic system)
• A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms
• A well-balanced positivity preserving ``second-order scheme for shallow water flows on unstructured meshes
• A kinetic scheme for the Saint-Venant system with a source term
• A family of stable numerical solvers for the shallow water equations with source terms.
• Some approximate Godunov schemes to compute shallow-water equations with topography.
• High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
• Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
• AQ-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system
• On Well‐Balanced Finite Volume Methods for Nonconservative Nonhomogeneous Hyperbolic Systems
• Godunov method for nonconservative hyperbolic systems
• On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
• Local Piecewise Hyperbolic Reconstruction of Numerical Fluxes for Nonlinear Scalar Conservation Laws
• Analysis and Approximation of Conservation Laws with Source Terms
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
• A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS
• A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations
• On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems
• High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. 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