Generalized finite difference method for two-dimensional shallow water equations

DOI10.1016/j.enganabound.2017.03.012zbMath1403.76133OpenAlexW2609412151MaRDI QIDQ1655824

Po-Wei Li, Chia-Ming Fan

Publication date: 10 August 2018

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2017.03.012

zbMATH Keywords

shallow water equationsRunge-Kutta methodgeneralized finite difference methodmeshless numerical schemesplit-coefficient matrix methods

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

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Cites Work

• Solving inverse Stokes problems by modified collocation Trefftz method
• The singular boundary method: mathematical background and application in orthotropic elastic problems
• On two upwind finite-difference schemes for hyperbolic equations in non- conservative form
• The \(\lambda\)-scheme
• Influence of several factors in the generalized finite difference method
• Improvements of generalized finite difference method and comparison with other meshless method
• Extrapolated local radial basis function collocation method for shallow water problems
• A regularized multi-level technique for solving potential problems by the method of fundamental solutions
• Application of the method of fundamental solutions to 2D and 3D Signorini problems
• Simulation of two-dimensional sloshing phenomenon by generalized finite difference method
• Singular boundary method using time-dependent fundamental solution for transient diffusion problems
• Compactly supported radial basis functions for shallow water equations.
• Solution of shallow-water equations using least-squares finite-element method
• Numerical solutions of boundary detection problems using modified collocation Trefftz method and exponentially convergent scalar homotopy algorithm
• Application of localized meshless methods to 2D shallow water equation problems
• Generalized finite difference method for solving two-dimensional non-linear obstacle problems
• Solving parabolic and hyperbolic equations by the generalized finite difference method
• Generalized Finite Difference Method for NumericalSolutions of Density-driven Groundwater Flows
• Generalized finite difference method for solving two-dimensional inverse Cauchy problems
• Open-Channel Flow

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