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...

In this paper, we present a fully discrete second-order finite-difference scheme with fast evaluation of the convolution involved in absorbing boundary conditions to solve one-dimensional linearized Green-Naghdi system. The Padé expansion square-root function complex plane is used implement convolution. By introducing constant damping parameter into governing equations, convergence analysis dev...

Abstract. We propose a mixed discontinuous Galerkin method for the bending problem of Naghdi shell, and present an analysis for its accuracy. The error estimate shows that when components of the curvature tensor and Christoffel symbols are piecewise linear functions, the finite element method has the optimal order of accuracy, which is uniform with respect to the shell thickness. Generally, the...

The hydroelastic response of mat-type Very Large Floating Structures (VLFSs) to severe sea conditions, such as tsunamis and hurricanes, must be assessed for safety and survivability. An efficient and robust nonlinear hydroelastic model is required to predict accurately the motion of and the dynamic loads on a VLFS due to such large waves. We develop a nonlinear theory to predict the hydroelasti...

A nonlinear theoretical model for deformations, oscillations, and drift motions of multiple elastic ice sheets in shallow waters due to combined waves uniform current is presented. The based on the Green–Naghdi theory fluid motion thin plate deformation sheets. In principle, there are N number floating with arbitrary lengths, drafts, rigidities, which may be located at distances from each other...

We describe in this work a discontinuous-Galerkin Finite-Element method to approximate the solutions of a new family of 1d Green-Naghdi models. These new models are shown to be more computationally efficient, while being asymptotically equivalent to the initial formulation with regard to the shallowness parameter. Using the free surface instead of the water height as a conservative variable, th...

We investigate linear stability of solitary waves of a Hamiltonian system. Unlike weakly nonlinear water wave models, the physical system considered here is nonlinearly dispersive, and contains nonlinearity in its highest derivative term. This results in more detailed asymptotic analysis of the eigenvalue problem in presence of a large parameter. Combining the technique of singular perturbation...