| Abstract: |
| We solve numerically the Serre-Green-Naghdi (SGN) system using stable, accurate and efficient fully discrete numerical schemes based on Galerkin/finite element methods. Although the SGN equations contain third-order derivatives, a modified Galerkin/finite element method allows the use of Lagrange finite elements and combined with explicit Runge-Kutta schemes for the discretization in time approximate solutions of the SGN system with variable bottom efficaciously. After reviewing the convergence properties of the new numerical scheme, a detailed study of the dynamics of the solitary waves of the SGN system over variable bottom topographies is presented. The effects of surface tension are also reviewed and new solutions are presented. |
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