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...

In this paper, we introduce artificial boundary conditions for the linearized Green-Naghdi system of equations. The derivation of such continuous (respectively discrete) boundary conditions include the inversion of Laplace transform (respectively Z-transform) and these boundary conditions are in turn non local in time. In the case of continuous boundary conditions, the inversion is done explici...

In the present investigation the disturbances in a homogeneous transversely isotropic magneto-Visco thermoelastic rotating medium with two temperature due to thermomechanical sources has been addressed. The thermoelasticity theories developed by Green-Naghdi (Type II and Type III) both with and without energy dissipation has been applied to the thermomechanical sources. The Laplace and Fourier ...

The free vibration analysis ofhomogeneous isotropic micropolar thermoelastic cylindrical curved plate in circumferential direction has been investigated in the context of generalized themoelasticity III, recently developed by Green and Naghdi. The model has been simplified using Helmholtz decomposition technique and the resulting equations have been solved using separation of variable method. M...