A dispersive wave hydro-morphodynamic model coupling the Green–Naghdi equations (the hydrodynamic part) with sediment continuity Exner equation morphodynamic is presented. Numerical solution algorithms based on discontinuous Galerkin finite element discretizations of are proposed. The include both coupled and decoupled approaches for solving parts simultaneously separately from each other, resp...

We consider strongly-nonlinear and weakly-dispersive surface water waves governed by equations of Boussinesq type, known as the Serre–Green–Naghdi system; it describes future states free depth averaged horizontal velocity, given their initial state. The lack knowledge velocity field well provided measurements lead to an ill-posed problem that cannot be solved traditional techniques. To this end...

In this paper, we introduce a discontinuous Finite Element formulation on simplicial unstructured meshes for the study of free surface flows based on the fully nonlinear and weakly dispersive GreenNaghdi equations. Working with a new class of asymptotically equivalent equations, which have a simplified analytical structure, we consider a decoupling strategy: we approximate the solutions of the ...

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 conserva...

Wave-induced oscillations of submerged horizontal plates are studied by conducting laboratory experiments and developing theoretical computational models. These models include a linear solver based on the Green-function method, nonlinear model Green–Naghdi wave equations, fluid dynamics. The plate oscillates in vertical direction due to oscillatory loads. Oscillations controlled use spring-damp...