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Well-balanced high-order finite difference methods for systems of balance laws

Journal of computational physics, 2021-01, Vol.425, p.109880, Article 109880

2021

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The Riemann problem for the shallow water equations with discontinuous topography: The wet–dry case

Journal of computational physics, 2019-02, Vol.378, p.344-365

2019

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Well-Balanced High-Order Finite Volume Methods for Systems of Balance Laws

Journal of scientific computing, 2020-02, Vol.82 (2), p.48, Article 48

2020

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Well-balanced adaptive compact approximate Taylor methods for systems of balance laws

Journal of computational physics, 2023-04, Vol.478, p.111979, Article 111979

2023

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Numerical Methods for Nonconservative Hyperbolic Systems: A Theoretical Framework

SIAM journal on numerical analysis, 2006-01, Vol.44 (1), p.300-321

Pares, Carlos

2006

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An almost fail-safe a-posteriori limited high-order CAT scheme

Journal of computational physics, 2024-02, Vol.498, p.112650, Article 112650

2024

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High-order well-balanced methods for systems of balance laws: a control-based approach

Applied mathematics and computation, 2021-04, Vol.394, p.125820, Article 125820

2021

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Recent Advances in Numerical Methods for Hyperbolic PDE Systems: NumHyp 2019

1st Edition 2021, 2021

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High-order fully well-balanced numerical methods for one-dimensional blood flow with discontinuous properties

Journal of computational physics, 2023-02, Vol.475, p.111869, Article 111869

2023

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Hyperbolic Problems: Theory, Numerics, Applications. Volume I: HYP2022, Malaga, Spain, June 20-24, 2022

2024th edition, 2024

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FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems

Computer methods in applied mechanics and engineering, 2010-01, Vol.199 (9), p.625-647

2010

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Hyperbolic Problems: Theory, Numerics, Applications. Volume II: HYP2022, Malaga, Spain, June 20-24, 2022

2024

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High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems

Mathematics of computation, 2006-07, Vol.75 (255), p.1103-1134

2006

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Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties

Journal of computational physics, 2013-06, Vol.242, p.53-85

2013

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ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows

Computers & fluids, 2009-10, Vol.38 (9), p.1731-1748

2009

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Progress in Industrial Mathematics: Success Stories: The Industry and the Academia Points of View

1st Edition 2021, 2021

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On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems

Applied mathematics and computation, 2021-01, Vol.388, p.125544, Article 125544

2021

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Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems

Journal of computational physics, 2021-11, Vol.444, p.110547, Article 110547

2021

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Arbitrarily High-Order (Weighted) Essentially Non-Oscillatory Finite Difference Schemes for Anelastic Flows on Staggered Meshes

Communications in computational physics, 2021-05, Vol.29 (5), p.1299-1335

2021

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On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas

Journal of computational physics, 2007-11, Vol.227 (1), p.574-601

2007

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In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension

Journal of computational physics, 2022-06, Vol.459, p.111152, Article 111152

2022

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Entropy-stable space–time DG schemes for non-conservative hyperbolic systems

ESAIM: Mathematical Modelling and Numerical Analysis, 2018-05, Vol.52 (3), p.995-1022

2018

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Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes

Journal of computational physics, 2008-09, Vol.227 (17), p.8107-8129

2008

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A Class of Well-Balanced Algorithms for Relativistic Fluids on a Schwarzschild Background

Journal of scientific computing, 2021-10, Vol.89 (1), p.3-43, Article 3

2021

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High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method

Numerical methods for partial differential equations, 2024-11, Vol.40 (6), p.n/a

2024

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Well-balanced high-order finite difference methods for systems of balance laws

The Riemann problem for the shallow water equations with discontinuous topography: The wet–dry case

Well-Balanced High-Order Finite Volume Methods for Systems of Balance Laws

Well-balanced adaptive compact approximate Taylor methods for systems of balance laws

Numerical Methods for Nonconservative Hyperbolic Systems: A Theoretical Framework

An almost fail-safe a-posteriori limited high-order CAT scheme

High-order well-balanced methods for systems of balance laws: a control-based approach

Recent Advances in Numerical Methods for Hyperbolic PDE Systems: NumHyp 2019

High-order fully well-balanced numerical methods for one-dimensional blood flow with discontinuous properties

Hyperbolic Problems: Theory, Numerics, Applications. Volume I: HYP2022, Malaga, Spain, June 20-24, 2022

FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems

Hyperbolic Problems: Theory, Numerics, Applications. Volume II: HYP2022, Malaga, Spain, June 20-24, 2022

High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems

Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties

ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows

Progress in Industrial Mathematics: Success Stories: The Industry and the Academia Points of View

On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems

Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems

Arbitrarily High-Order (Weighted) Essentially Non-Oscillatory Finite Difference Schemes for Anelastic Flows on Staggered Meshes

On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas

In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension

Entropy-stable space–time DG schemes for non-conservative hyperbolic systems

Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes

A Class of Well-Balanced Algorithms for Relativistic Fluids on a Schwarzschild Background

High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method

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