A reconstructed central discontinuous Galerkin-finite element method for the fully nonlinear weakly dispersive Green-Naghdi model

DOI10.1016/j.apnum.2016.08.008zbMath1462.65139OpenAlexW2511998430MaRDI QIDQ321371

Haiyun Dong, Maojun Li

Publication date: 13 October 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2016.08.008

zbMATH Keywords

finite element methodscomputational costGreen-Naghdi modelcentral discontinuous Galerkin methodshigh order methods

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items

Combined hybridizable discontinuous Galerkin (HDG) and Runge-Kutta discontinuous Galerkin (RK-DG) formulations for Green-Naghdi equations on unstructured meshes ⋮ A reconstructed central discontinuous Galerkin method for conservation laws ⋮ A new symmetric interior penalty discontinuous Galerkin formulation for the <scp>Serre–Green–Naghdi</scp> equations ⋮ Unnamed Item ⋮ Numerical scheme for the generalised Serre-Green-Naghdi model ⋮ Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows ⋮ The solution of nonlinear Green-Naghdi equation arising in water sciences via a meshless method which combines moving Kriging interpolation shape functions with the weighted essentially non-oscillatory method ⋮ A new model of shoaling and breaking waves: one-dimensional solitary wave on a mild sloping beach ⋮ A High Order Central DG method of the Two-Layer Shallow Water Equations ⋮ A positivity-preserving well-balanced central discontinuous Galerkin method for the nonlinear shallow water equations ⋮ A discontinuous Galerkin method for a new class of Green-Naghdi equations on simplicial unstructured meshes ⋮ Maximum-principle-satisfying and positivity-preserving high order central DG methods on unstructured overlapping meshes for two-dimensional hyperbolic conservation laws

Cites Work

• High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model
• Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations
• Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field
• Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model
• A central discontinuous Galerkin method for Hamilton-Jacobi equations
• A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Long-time effects of bottom topography in shallow water
• Recent advances in Serre-Green-Naghdi modelling for wave transformation, breaking and runup processes
• A numerical scheme for the Green-Naghdi model
• High order central discontinuous Galerkin-finite element methods for the Camassa-Holm equation
• A pseudo-spectral algorithm and test cases for the numerical solution of the two-dimensional rotating Green-Naghdi shallow water equations
• Central local discontinuous galerkin methods on overlapping cells for diffusion equations
• A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: boundary conditions and validation
• A derivation of equations for wave propagation in water of variable depth
• Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation
• Central Discontinuous Galerkin Methods on Overlapping Cells with a Nonoscillatory Hierarchical Reconstruction
• A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: model development and analysis