GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations | Paper Citation Record

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This paper cites Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems

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This paper cites Bona-Smith-Type systems in Bounded Domains with Slip-WallBoundaryConditions:TheoreticalJustificationandaConservativeNumericalScheme.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Bona-Smith-Type systems in Bounded Domains with Slip-WallBoundaryConditions:TheoreticalJustificationandaConservativeNumericalScheme

Reference 2

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators

Reference 3

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Julia:AFreshApproachtoNumerical Computing

Reference 4

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This paper cites On High Order ADER Discontinuous Galerkin Schemes for First Order Hyperbolic Reformulations of Nonlinear Dispersive Systems.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations On High Order ADER Discontinuous Galerkin Schemes for First Order Hyperbolic Reformulations of Nonlinear Dispersive Systems

Reference 5

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This paper cites Entropy Stable Spectral Collo- cationSchemesfortheNavier-StokesEquations:DiscontinuousInterfaces.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Entropy Stable Spectral Collo- cationSchemesfortheNavier-StokesEquations:DiscontinuousInterfaces

Reference 6

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This paper cites Time-StableBoundaryConditionsforFinite- Difference Schemes Solving Hyperbolic Systems: Methodology and Application to High- Order Compact Schemes.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Time-StableBoundaryConditionsforFinite- Difference Schemes Solving Hyperbolic Systems: Methodology and Application to High- Order Compact Schemes

Reference 7

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This paper cites Dispersive and dispersive-like bores in channels with sloping banks.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Dispersive and dispersive-like bores in channels with sloping banks

Reference 8

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This paper cites Plots.jl–auser extendable plotting API for the Julia programming language.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Plots.jl–auser extendable plotting API for the Julia programming language

Reference 9

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This paper cites KernelAbstractions.jl.DOI: 10.5281/zenodo.4021259.URL: https://github.com/ JuliaGPU/KernelAbstractions.jl.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations KernelAbstractions.jl.DOI: 10.5281/zenodo.4021259.URL: https://github.com/ JuliaGPU/KernelAbstractions.jl

Reference 10

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This paper cites Solitary water wave in- teractions.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Solitary water wave in- teractions

Reference 11

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Unresolved cited work

Reference 12

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Unresolved cited work

Reference 13

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Observation fa1ab944-e71b-42b3-a3db-d0b2e6ef5976 · outbound

This paper cites Rigorous justification of the Favrie–Gavrilyuk approximation to the Serre– Green–Naghdi model.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Rigorous justification of the Favrie–Gavrilyuk approximation to the Serre– Green–Naghdi model

Reference 14

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This paper cites Finitevolumeandpseudo-spectral schemesforthefullynonlinear1DSerreequations.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Finitevolumeandpseudo-spectral schemesforthefullynonlinear1DSerreequations

Reference 15

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This paper cites Finite volume schemes for dispersive wave propagation and runup.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Finite volume schemes for dispersive wave propagation and runup

Reference 16

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Observation 017be5be-4497-4fd3-82e9-d48a25b41600 · outbound

This paper cites Unsteady undular bores in fully nonlinear shallow-water theory.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Unsteady undular bores in fully nonlinear shallow-water theory

Reference 17

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This paper cites An efficient hyperbolic relaxation system for dispersivenon-hydrostaticwaterwavesanditssolutionwithhighorderdiscontinuousGalerkin schemes.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations An efficient hyperbolic relaxation system for dispersivenon-hydrostaticwaterwavesanditssolutionwithhighorderdiscontinuousGalerkin schemes

Reference 18

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This paper cites Activefluxschemes.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Activefluxschemes

Reference 19

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This paper cites Étude théorique et expérimentale des ondes de translation dans les canaux découverts.Paris: Dunod, 1935.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Étude théorique et expérimentale des ondes de translation dans les canaux découverts.Paris: Dunod, 1935

Reference 20

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This paper cites A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves

Reference 21

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This paper cites Review of summation-by-parts opera- torswithsimultaneousapproximationtermsforthenumericalsolutionofpartialdifferential equations.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Review of summation-by-parts opera- torswithsimultaneousapproximationtermsforthenumericalsolutionofpartialdifferential equations

Reference 22

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Discretelycon- servativefinite-differenceformulationsfornonlinearconservationlawsinsplitform:Theory and boundary conditions

Reference 23

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This paper cites Classroom Note:Calculation of Weights in Finite Difference Formulas.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Classroom Note:Calculation of Weights in Finite Difference Formulas

Reference 24

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This paper cites A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods

Reference 25

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Stationaryshock-liketransition fronts in dispersive systems

Reference 26

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This paper cites 2D Serre-Green-Naghdi equations over topography: Elliptic operatorinversionmethod.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations 2D Serre-Green-Naghdi equations over topography: Elliptic operatorinversionmethod

Reference 27

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Observation ba03ea27-cb97-49da-881e-4b0768fc600e · outbound

This paper cites Dispersion of tsunamis: does it really matter?.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Dispersion of tsunamis: does it really matter?

Reference 28

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This paper cites A derivation of equations for wave propagation in water of variable depth.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A derivation of equations for wave propagation in water of variable depth

Reference 29

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This paper cites Hyperbolicrelaxationtechniqueforsolving the dispersive Serre-Green-Naghdi equations with topography.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Hyperbolicrelaxationtechniqueforsolving the dispersive Serre-Green-Naghdi equations with topography

Reference 30

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This paper cites Well-balanced second-order convex lim- iting technique for solving the Serre-Green-Naghdi equations.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Well-balanced second-order convex lim- iting technique for solving the Serre-Green-Naghdi equations

Reference 31

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This paper cites MultidimensionalSummation-by-PartsOp- erators: General Theory and Application to Simplex Elements.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations MultidimensionalSummation-by-PartsOp- erators: General Theory and Application to Simplex Elements

Reference 32

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This paper cites Constructing stable, high-order finite-difference operators on point clouds over complex geometries.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Constructing stable, high-order finite-difference operators on point clouds over complex geometries

Reference 33

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Entropy-stable, high-order summation-by-parts discretizations without inter- face penalties

Reference 34

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This paper cites A Flux Reconstruction Approach to High-Order Schemes Including Discon- tinuous Galerkin Methods.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A Flux Reconstruction Approach to High-Order Schemes Including Discon- tinuous Galerkin Methods

Reference 35

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This paper cites One dimensional modelling of Favre waves in channels.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations One dimensional modelling of Favre waves in channels

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Observation 69951c71-ed3a-4d7e-88a0-e657e5ce0bf0 · outbound

This paper cites Low dispersion finite volume/element dis- cretization of the enhanced Green–Naghdi equations for wave propagation, breaking and runup on unstructured meshes.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Low dispersion finite volume/element dis- cretization of the enhanced Green–Naghdi equations for wave propagation, breaking and runup on unstructured meshes

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This paper cites Full Nonlinearity in Weakly Dispersive Boussinesq Models: Luxury or Necessity.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Full Nonlinearity in Weakly Dispersive Boussinesq Models: Luxury or Necessity

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Finite element and finite difference methods for hyperbolic partial differential equations

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A robust first order meshfree method for time-dependent nonlinear conservation laws

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations

Reference 41

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GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Summation by parts operators for finite difference approxi- mations of second derivatives

Reference 42

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correction dated 2017-09-29. Source: crossref record 10.1016/j.jcp.2017.09.051->10.1016/j.jcp.2004.03.001:correction, observed 2026-07-11T03:18:02.403647+00:00. This notice travels one citation hop only.

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This paper cites AmodifiedGalerkin/finiteelementmethod forthenumericalsolutionoftheSerre-Green-Naghdisystem.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations AmodifiedGalerkin/finiteelementmethod forthenumericalsolutionoftheSerre-Green-Naghdisystem

Reference 43

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Observation f3cc33e3-cb37-442b-a369-be0bcdce7f04 · outbound

This paper cites A conservative fully-discrete numerical method for the regularised shallow water wave equations.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A conservative fully-discrete numerical method for the regularised shallow water wave equations

Reference 44

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Observation 375c2cf5-233d-4170-8081-d6ac2861972b · outbound

This paper cites A Class of Boundary Conditions for Time-Discrete Green-NaghdiEquationswithBathymetry.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A Class of Boundary Conditions for Time-Discrete Green-NaghdiEquationswithBathymetry

Reference 45

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Observation a0f49f41-2acf-4199-b07d-f1a5f20d6f71 · outbound

This paper cites Finitevolumeapproximationsandstrictstabilityforhyperbolic problems.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Finitevolumeapproximationsandstrictstabilityforhyperbolic problems

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This paper cites Entropy-satisfying scheme for a hierarchy of dispersive reduced models of free surface flow.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Entropy-satisfying scheme for a hierarchy of dispersive reduced models of free surface flow

Reference 47

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This paper cites DifferentialEquations.jl–APerformantandFeature-RichEcosys- tem for Solving Differential Equations in Julia.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations DifferentialEquations.jl–APerformantandFeature-RichEcosys- tem for Solving Differential Equations in Julia

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Observation b1844175-64d5-48c2-976f-2a840878f61f · outbound

This paper cites Structure-Preserving Approximations of the Serre-Green- Naghdi Equations in Standard and Hyperbolic Form.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Structure-Preserving Approximations of the Serre-Green- Naghdi Equations in Standard and Hyperbolic Form

Reference 49

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Observation 96159504-3c35-42d4-804f-b69b5c9ca7f5 · outbound

This paper cites Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations

Reference 50

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Observation 7027eb80-c670-4aba-a6f5-4f86e42d62d4 · outbound

This paper cites Mimeticpropertiesofdifferenceoperators:productandchainrulesasforfunc- tions of bounded variation and entropy stability of second derivatives.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Mimeticpropertiesofdifferenceoperators:productandchainrulesasforfunc- tions of bounded variation and entropy stability of second derivatives

Reference 51

Resolution: verified exact; doi, observed 2026-08-03T12:43:41.949408Z

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Observation e48adc13-9df4-4b04-926a-fef7236b6c74 · outbound

This paper cites SBPoperatorsforCPRmethods.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations SBPoperatorsforCPRmethods

Reference 52

Resolution: verified exact; doi, observed 2026-08-03T12:43:41.817418Z

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Observation 76bd5a92-7a6f-40f0-9a5d-92cd53d17cee · outbound

This paper cites Shallow water equations: Split-form, entropy stable, well-balanced, and posi- tivity preserving numerical methods.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Shallow water equations: Split-form, entropy stable, well-balanced, and posi- tivity preserving numerical methods

Reference 53

Resolution: verified exact; doi, observed 2026-08-03T12:43:41.666257Z

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Observation c39c64be-d8e1-4a38-8607-ac23779c174f · outbound

This paper cites Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:32.377931Z

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Observation 124b8fcc-4232-40c8-b9af-c560a0b90c66 · outbound

This paper cites A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations

Reference 55

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Observation b8c95792-48bc-4142-951d-982a837b0d41 · outbound

This paper cites Summation-by-parts operators for correction procedure via reconstruction.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Summation-by-parts operators for correction procedure via reconstruction

Reference 56

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Observation f1d6dd2c-f157-4811-a068-d28da230647a · outbound

This paper cites Contribution à l’étude des écoulements permanents et variables dans les canaux.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Contribution à l’étude des écoulements permanents et variables dans les canaux

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:32.639057Z

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Observation 5f1e3f31-b515-480a-a115-f59a5c3feed0 · outbound

This paper cites Summation by Parts for Finite Difference Approximations for𝑑/ 𝑑𝑥.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Summation by Parts for Finite Difference Approximations for𝑑/ 𝑑𝑥

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:32.702845Z

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Observation c0a680b1-846e-4a90-b1cf-76c97ff11aea · outbound

This paper cites A novel energy-bounded Boussinesq model and a well balanced and stable numerical discretisation.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A novel energy-bounded Boussinesq model and a well balanced and stable numerical discretisation

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:32.763828Z

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Observation f05cd1e0-4880-4224-ab24-9213b7a4945d · outbound

This paper cites Review of summation-by-parts schemes for initial-boundary- value problems.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Review of summation-by-parts schemes for initial-boundary- value problems

Reference 60

Resolution: malformed identifier; no resolver link, observed 2026-08-03T12:41:32.838904Z

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Observation 1b3961f3-0970-45d9-8057-d87834aff6c2 · outbound

This paper cites Extended Lagrangian approach for the numer- ical study of multidimensional dispersive waves: Applications to the Serre-Green-Naghdi equations.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Extended Lagrangian approach for the numer- ical study of multidimensional dispersive waves: Applications to the Serre-Green-Naghdi equations

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:33.006643Z

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Observation 4d447c45-c1db-474c-8680-281d501cddae · outbound

This paper cites Undular bores (Favre-waves) in open channels – Experimental studies.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Undular bores (Favre-waves) in open channels – Experimental studies

Reference 63

Resolution: verified exact; doi, observed 2026-08-03T12:43:41.492647Z

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Observation b73d7699-64e4-47f1-b46d-ea52aedafa5e · outbound

This paper cites A New Class of High-Order Energy Stable Flux Reconstruction Schemes.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A New Class of High-Order Energy Stable Flux Reconstruction Schemes

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:33.243272Z

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Observation 19691530-a5e0-47bc-b22c-b015d03597c7 · outbound

This paper cites A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves

Reference 65

Resolution: verified exact; doi, observed 2026-08-03T12:43:41.352993Z

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Observation b57176d6-49e2-4e06-9aee-b761326ec703 · outbound

This paper cites An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on un- structured curvilinear meshes with discontinuous bathymetry.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on un- structured curvilinear meshes with discontinuous bathymetry

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:33.379223Z

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Observation 57575e0d-6334-47f4-9a5f-321a8f0d7c74 · outbound

This paper cites Wittenstein, V.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Wittenstein, V

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:33.448379Z

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Observation 3625b8c1-1625-47ce-b7f8-f0678cec6e95 · outbound

This paper cites an unresolved cited work.

GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations Unresolved cited work

Reference 531

Resolution: verified exact; doi, observed 2026-08-03T12:43:42.161861Z

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