A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system
For researchers in coastal engineering and wave modeling, this method simplifies the numerical solution of a complex system, but it is an incremental improvement over existing finite element approaches.
The paper proposes a modified Galerkin/finite element method for solving the fully nonlinear Serre-Green-Naghdi shallow water wave equations, enabling the use of low-order Lagrange elements despite third-order derivatives. The method is validated against laboratory experiments and theoretical results, showing good agreement.
A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the fact that the system contains third order spatial partial derivatives for the depth averaged velocity of the fluid. After studying the efficacy and the conservation properties of the new numerical method, we proceed with the validation of the new numerical model and boundary conditions by comparing the numerical solutions with laboratory experiments and with available theoretical asymptotic results.