International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 04/2019, Volume 89, Issue 11, pp. 465 - 482

Summary We present a well‐balanced finite volume scheme for the compressible Euler equations with gravity, where the approximate Riemann solver is derived...

robustness | Euler equations with gravity | well‐balanced scheme | finite volume methods | relaxation | well-balanced scheme | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EXPLICIT STEADY-STATES | PHYSICS, FLUIDS & PLASMAS | STABILITY | Economic models | Gravitation | Boundary value problems | Compressibility | Dimensions | Properties | Euler-Lagrange equation | Equilibrium | Equations | Robustness (mathematics) | Solutions | Volume | Riemann solver | Gravity | Mathematics - Numerical Analysis

robustness | Euler equations with gravity | well‐balanced scheme | finite volume methods | relaxation | well-balanced scheme | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EXPLICIT STEADY-STATES | PHYSICS, FLUIDS & PLASMAS | STABILITY | Economic models | Gravitation | Boundary value problems | Compressibility | Dimensions | Properties | Euler-Lagrange equation | Equilibrium | Equations | Robustness (mathematics) | Solutions | Volume | Riemann solver | Gravity | Mathematics - Numerical Analysis

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 05/2013, Volume 72, Issue 2, pp. 177 - 205

SUMMARYWe are interested in simulating blood flow in arteries with a one‐dimensional model. Thanks to recent developments in the analysis of hyperbolic system...

well‐balanced scheme | semi‐analytical solutions | man at eternal rest | hydrostatic reconstruction | blood flow simulation | shallow water | finite volume scheme | Finite volume scheme | Hydrostatic reconstruction | Man at eternal rest | Semi-analytical solutions | Blood flow simulation | Well-balanced scheme | Shallow water | WALL SHEAR-STRESS | UPWIND SCHEMES | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | SAINT-VENANT SYSTEM | well-balanced scheme | semi-analytical solutions | SHALLOW-WATER EQUATIONS | SOURCE TERMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | UNSTRUCTURED MESHES | ARTERIAL NETWORKS | HYPERBOLIC CONSERVATION-LAWS | WAVE-PROPAGATION | Analysis | Blood flow | Shallow water equations | Rest | Computer simulation | Mathematical analysis | Preserves | Mathematical models | Arteries

well‐balanced scheme | semi‐analytical solutions | man at eternal rest | hydrostatic reconstruction | blood flow simulation | shallow water | finite volume scheme | Finite volume scheme | Hydrostatic reconstruction | Man at eternal rest | Semi-analytical solutions | Blood flow simulation | Well-balanced scheme | Shallow water | WALL SHEAR-STRESS | UPWIND SCHEMES | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | SAINT-VENANT SYSTEM | well-balanced scheme | semi-analytical solutions | SHALLOW-WATER EQUATIONS | SOURCE TERMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | UNSTRUCTURED MESHES | ARTERIAL NETWORKS | HYPERBOLIC CONSERVATION-LAWS | WAVE-PROPAGATION | Analysis | Blood flow | Shallow water equations | Rest | Computer simulation | Mathematical analysis | Preserves | Mathematical models | Arteries

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 06/2015, Volume 78, Issue 6, pp. 355 - 383

SummaryShallow water models are widely used to describe and study free‐surface water flow. While in some practical applications the bottom friction does not...

central‐upwind scheme | well‐balanced scheme | shallow water equations with friction terms | Shallow water equations with friction terms | Central-upwind scheme | Well-balanced scheme | HYPERBOLIC SYSTEMS | PHYSICS, FLUIDS & PLASMAS | RECONSTRUCTION | EQUATIONS | SAINT-VENANT SYSTEM | FLUX | well-balanced scheme | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MODELS | CONSERVATION-LAWS | central-upwind scheme | Water | Hydrology | Houses | Computer simulation | Friction | Rain water | Mathematical models | Runge-Kutta method | Water depth | Preserving

central‐upwind scheme | well‐balanced scheme | shallow water equations with friction terms | Shallow water equations with friction terms | Central-upwind scheme | Well-balanced scheme | HYPERBOLIC SYSTEMS | PHYSICS, FLUIDS & PLASMAS | RECONSTRUCTION | EQUATIONS | SAINT-VENANT SYSTEM | FLUX | well-balanced scheme | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MODELS | CONSERVATION-LAWS | central-upwind scheme | Water | Hydrology | Houses | Computer simulation | Friction | Rain water | Mathematical models | Runge-Kutta method | Water depth | Preserving

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 03/2019, Volume 89, Issue 8, pp. 304 - 325

Summary High‐order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite...

path‐conservative scheme | well‐balanced scheme | CWENO reconstruction | shallow water equations | finite volume scheme | well-balanced scheme | path-conservative scheme | PHYSICS, FLUIDS & PLASMAS | IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | FULL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | CENTRAL WENO SCHEME | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Reconstruction | Shallow water equations | Conservation laws | Accuracy | Computer simulation | Solutions | Volume | Procedures | Shallow water | Equations

path‐conservative scheme | well‐balanced scheme | CWENO reconstruction | shallow water equations | finite volume scheme | well-balanced scheme | path-conservative scheme | PHYSICS, FLUIDS & PLASMAS | IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | FULL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | CENTRAL WENO SCHEME | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Reconstruction | Shallow water equations | Conservation laws | Accuracy | Computer simulation | Solutions | Volume | Procedures | Shallow water | Equations

Journal Article

SIAM JOURNAL ON SCIENTIFIC COMPUTING, ISSN 1064-8275, 2019, Volume 41, Issue 3, pp. A1500 - A1526

We present a positive-and asymptotic-preserving numerical scheme for solving linear kinetic transport equations that relax to a diffusive equation in the limit...

asymptotic-preserving schemes | MATHEMATICS, APPLIED | positive-preserving schemes | DG-IMEX SCHEMES | AP SCHEMES | RUNGE-KUTTA METHODS | WELL-BALANCED SCHEMES | finite difference methods | diffusion limit | DIFFUSIVE RELAXATION SCHEMES | RADIATIVE-TRANSFER | kinetic transport equations | BOLTZMANN-EQUATION | MOMENT CLOSURES | CONSERVATION-LAWS | OPTICALLY THICK | BASIC BIOLOGICAL SCIENCES | asymptotic | nite difference methods | preserving schemes

asymptotic-preserving schemes | MATHEMATICS, APPLIED | positive-preserving schemes | DG-IMEX SCHEMES | AP SCHEMES | RUNGE-KUTTA METHODS | WELL-BALANCED SCHEMES | finite difference methods | diffusion limit | DIFFUSIVE RELAXATION SCHEMES | RADIATIVE-TRANSFER | kinetic transport equations | BOLTZMANN-EQUATION | MOMENT CLOSURES | CONSERVATION-LAWS | OPTICALLY THICK | BASIC BIOLOGICAL SCIENCES | asymptotic | nite difference methods | preserving schemes

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 12/2016, Volume 110, pp. 26 - 40

This paper presents a finite volume scheme for a scalar one-dimensional fluid–particle interaction model. When devising a finite volume scheme for this model,...

Solid–fluid interaction | Finite volume scheme | Moving mesh scheme | Moving interface | Well-balanced scheme | Singular source term | PDE-ODE coupling | Burgers equation | MATHEMATICS, APPLIED | Solid-fluid interaction | MODEL

Solid–fluid interaction | Finite volume scheme | Moving mesh scheme | Moving interface | Well-balanced scheme | Singular source term | PDE-ODE coupling | Burgers equation | MATHEMATICS, APPLIED | Solid-fluid interaction | MODEL

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2015, Volume 290, pp. 188 - 218

In this work, an ADER type finite volume numerical scheme is proposed as an extension of a first order solver based on weak solutions of RPs with source terms....

Roe solver | Burgers | High order accuracy | Energy balanced | Well balanced | Shallow water | ADER | GENERALIZED RIEMANN PROBLEM | EFFICIENT IMPLEMENTATION | WENO SCHEMES | RIVER FLOW | PHYSICS, MATHEMATICAL | NONOSCILLATORY SCHEMES | MOVING WATER | SHOCK-CAPTURING SCHEMES | SOURCE TERMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HYPERBOLIC CONSERVATION-LAWS | DISCONTINUOUS TOPOGRAPHY | Shallow water equations | Accuracy | Balancing | Discretization | Computation | Mathematical analysis | Exact solutions | Solvers | Mathematical models

Roe solver | Burgers | High order accuracy | Energy balanced | Well balanced | Shallow water | ADER | GENERALIZED RIEMANN PROBLEM | EFFICIENT IMPLEMENTATION | WENO SCHEMES | RIVER FLOW | PHYSICS, MATHEMATICAL | NONOSCILLATORY SCHEMES | MOVING WATER | SHOCK-CAPTURING SCHEMES | SOURCE TERMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HYPERBOLIC CONSERVATION-LAWS | DISCONTINUOUS TOPOGRAPHY | Shallow water equations | Accuracy | Balancing | Discretization | Computation | Mathematical analysis | Exact solutions | Solvers | Mathematical models

Journal Article

SIAM Journal of Scientific Computing, ISSN 1064-8275, 2004, Volume 25, Issue 6, pp. 2050 - 2065

We consider the Saint-Venant system for shallow water flows, with non. at bottom. It is a hyperbolic system of conservation laws that approximately describes...

Shallow water equations | Well-balanced schemes | Finite volume schemes | SOURCE TERMS | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | SAINT-VENANT | well-balanced schemes | SCALAR CONSERVATION-LAWS | shallow water equations | EQUATIONS | finite volume schemes | KINETIC SCHEME

Shallow water equations | Well-balanced schemes | Finite volume schemes | SOURCE TERMS | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | SAINT-VENANT | well-balanced schemes | SCALAR CONSERVATION-LAWS | shallow water equations | EQUATIONS | finite volume schemes | KINETIC SCHEME

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2017, Volume 55, Issue 2, pp. 758 - 784

A key difficulty in the analysis and numerical approximation of the shallow water equations is the nonconservative product of measures due to the gravitational...

Shallow water equations | Nonconservative products of measures | Semi discrete entropy inequality | Well-balanced property | Wet-dry front | Water at rest | water at rest | MATHEMATICS, APPLIED | wet-dry front | NONCONSERVATIVE PRODUCTS | semi discrete entropy inequality | SHALLOW-WATER EQUATIONS | SOURCE TERMS | ORDER | well-balanced property | shallow water equations | nonconservative products of measures | SYSTEMS | FLOWS | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES

Shallow water equations | Nonconservative products of measures | Semi discrete entropy inequality | Well-balanced property | Wet-dry front | Water at rest | water at rest | MATHEMATICS, APPLIED | wet-dry front | NONCONSERVATIVE PRODUCTS | semi discrete entropy inequality | SHALLOW-WATER EQUATIONS | SOURCE TERMS | ORDER | well-balanced property | shallow water equations | nonconservative products of measures | SYSTEMS | FLOWS | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES

Journal Article

Environmental Modelling and Software, ISSN 1364-8152, 04/2015, Volume 66, pp. 131 - 152

The aim of this paper is to present a novel monotone upstream scheme for conservation law (MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is...

Shallow water equations | MUSCL scheme | Finite volume method | Unstructured grids | Godunov-type model | SOURCE-TERM TREATMENT | FINITE-VOLUME MODEL | RESIDUAL DISTRIBUTION | WELL-BALANCED SCHEME | FLOW MODEL | SOLUTE TRANSPORT | ENVIRONMENTAL SCIENCES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPLEX TOPOGRAPHY | ENGINEERING, ENVIRONMENTAL | GODUNOV-TYPE | HIGH-RESOLUTION | HYPERBOLIC CONSERVATION-LAWS | Usage | Environmental law | Analysis | Mathematical analysis | Conservation | Preserves | Software | Mathematical models | Two dimensional | MUSCL schemes | Computer programs

Shallow water equations | MUSCL scheme | Finite volume method | Unstructured grids | Godunov-type model | SOURCE-TERM TREATMENT | FINITE-VOLUME MODEL | RESIDUAL DISTRIBUTION | WELL-BALANCED SCHEME | FLOW MODEL | SOLUTE TRANSPORT | ENVIRONMENTAL SCIENCES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPLEX TOPOGRAPHY | ENGINEERING, ENVIRONMENTAL | GODUNOV-TYPE | HIGH-RESOLUTION | HYPERBOLIC CONSERVATION-LAWS | Usage | Environmental law | Analysis | Mathematical analysis | Conservation | Preserves | Software | Mathematical models | Two dimensional | MUSCL schemes | Computer programs

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2020, Volume 366, p. 124748

A van Leer-type numerical scheme for a model of two-phase flows is constructed. The governing equations were derived from the modeling of...

Numerical approximation | van Leer scheme | Accuracy | Nonconservative | Two-phase flow | Well-balanced scheme

Numerical approximation | van Leer scheme | Accuracy | Nonconservative | Two-phase flow | Well-balanced scheme

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 03/2018, Volume 86, Issue 7, pp. 491 - 508

Summary The blood flow model in arteries admits the steady state solutions, for which the flux gradient is nonzero, and is exactly balanced by the source term....

blood flow model | well‐balanced property | discontinuous Galerkin method | source term | hydrostatic reconstruction | finite volume WENO scheme | well-balanced property | HYPERBOLIC SYSTEMS | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | SOURCE TERMS | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | GAS-KINETIC SCHEME | NUMERICAL SCHEMES | WAVE-PROPAGATION | Analysis | Arteries | Methods | Blood flow | Reconstruction | Methodology | Steady state | Equilibrium | Blood | Accuracy | Solutions | Volume | Essentially non-oscillatory schemes | Mathematical models | Galerkin method

blood flow model | well‐balanced property | discontinuous Galerkin method | source term | hydrostatic reconstruction | finite volume WENO scheme | well-balanced property | HYPERBOLIC SYSTEMS | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | SOURCE TERMS | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | GAS-KINETIC SCHEME | NUMERICAL SCHEMES | WAVE-PROPAGATION | Analysis | Arteries | Methods | Blood flow | Reconstruction | Methodology | Steady state | Equilibrium | Blood | Accuracy | Solutions | Volume | Essentially non-oscillatory schemes | Mathematical models | Galerkin method

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 02/2017, Volume 112, pp. 65 - 78

We investigate the performance of the high order well-balanced hybrid compact-weighted essentially non-oscillatory (WENO) finite difference scheme (Hybrid) for...

Shallow water equations | Hybrid | Multi-resolution | WENO-Z | Compact | Well-balanced | MATHEMATICS, APPLIED | ENO | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | FINITE-DIFFERENCE SCHEME | SOURCE TERMS | LAWS | EXACT CONSERVATION PROPERTY | Marine geography | Analysis

Shallow water equations | Hybrid | Multi-resolution | WENO-Z | Compact | Well-balanced | MATHEMATICS, APPLIED | ENO | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | FINITE-DIFFERENCE SCHEME | SOURCE TERMS | LAWS | EXACT CONSERVATION PROPERTY | Marine geography | Analysis

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 05/2016, Volume 81, Issue 2, pp. 104 - 127

Summary This paper describes a numerical discretization of the compressible Euler equations with a gravitational potential. A pertinent feature of the...

steady states | relaxation schemes | source terms | Euler flow | well‐balanced schemes | hyperbolic system | Source terms | Well-balanced schemes | Hyperbolic system | Relaxation schemes | Steady states | Gravitation | Hydrostatics | Approximation | Discretization | Mathematical analysis | Mathematical models | Entropy | Euler equations

steady states | relaxation schemes | source terms | Euler flow | well‐balanced schemes | hyperbolic system | Source terms | Well-balanced schemes | Hyperbolic system | Relaxation schemes | Steady states | Gravitation | Hydrostatics | Approximation | Discretization | Mathematical analysis | Mathematical models | Entropy | Euler equations

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2014, Volume 259, pp. 199 - 219

Well-balanced high-order finite volume schemes are designed to approximate the Euler equations with gravitation. The schemes preserve discrete equilibria,...

Source terms | Well-balanced schemes | Hydrodynamics | Numerical methods | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SHALLOW-WATER FLOWS | RECONSTRUCTION | PHYSICS, MATHEMATICAL | FINITE-VOLUME SCHEMES | WAVE-PROPAGATION | ACCURACY | Gravity | Reconstruction | Gravitation | Hydrostatics | Approximation | Mathematical analysis | Euler equations | Computational efficiency | Steady state

Source terms | Well-balanced schemes | Hydrodynamics | Numerical methods | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SHALLOW-WATER FLOWS | RECONSTRUCTION | PHYSICS, MATHEMATICAL | FINITE-VOLUME SCHEMES | WAVE-PROPAGATION | ACCURACY | Gravity | Reconstruction | Gravitation | Hydrostatics | Approximation | Mathematical analysis | Euler equations | Computational efficiency | Steady state

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2018, Volume 362, pp. 425 - 448

We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and...

Shallow water equations | Wetting and drying | Discontinuous Galerkin method | Non-conforming mesh | Well-balanced scheme | Curved mesh | GRIDS | PHYSICS, MATHEMATICAL | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | FLOWS | EULER EQUATIONS | Tsunamis | Models | Numerical analysis

Shallow water equations | Wetting and drying | Discontinuous Galerkin method | Non-conforming mesh | Well-balanced scheme | Curved mesh | GRIDS | PHYSICS, MATHEMATICAL | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | FLOWS | EULER EQUATIONS | Tsunamis | Models | Numerical analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 03/2017, Volume 332, pp. 475 - 491

The gas dynamics under gravitational field is usually associated with multiple scale nature due to large density variation and a wide variation of local...

Non-equilibrium phenomena | Gravitational field | Well-balanced property | Unified gas-kinetic scheme | Multi-scale flow | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EQUATIONS | CONTINUUM | RAREFIED FLOWS | PHYSICS, MATHEMATICAL | Physics - Computational Physics

Non-equilibrium phenomena | Gravitational field | Well-balanced property | Unified gas-kinetic scheme | Multi-scale flow | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EQUATIONS | CONTINUUM | RAREFIED FLOWS | PHYSICS, MATHEMATICAL | Physics - Computational Physics

Journal Article