Discontinuous Galerkin methods for solving Boussinesq-Green-Naghdi equations in resolving non-linear and dispersive surface water waves. (English) Zbl 1351.76074
Summary: A local discontinuous Galerkin method for Boussinesq-Green-Naghdi equations is presented and validated against experimental results for wave transformation over a submerged shoal. Currently Green-Naghdi equations have many variants. In this paper a numerical method in one dimension is presented for the Green-Naghdi equations based on rotational characteristics in the velocity field. Stability criterion is also established for the linearized Green-Naghdi equations for both the analytical problem and the numerical method. Verification is done against a linearized standing wave problem in flat bathymetry and \(h\) , \(p\) (denoted by \(K\) in this paper) error rates are plotted. Validation plots show good agreement of the numerical results with the experimental ones.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
rotational Boussinesq-Green-Naghdi; discontinuous Galerkin; mixed space-time derivatives; unstructured mesh; surf-zone; non-conservativeReferences:
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