A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system

Dimitrios Mitsotakis (1) , Costas Synolakis (2) , Mark Mcguinness (1)

1 Victoria University of Wellington
2 USC - University of Southern California

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.

Mots clés: Solitary waves; Green-Naghdi system; Finite element methods; Serre equations

Domaines: Analyse numérique [math.NA]

Dimitrios Mitsotakis, Costas Synolakis, Mark Mcguinness. A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system. 2016. ⟨hal-01152498v2⟩