In this dissertation a moving mesh method finite element method is used to approximate moving boundary solutions to the shallow water equations. An Arbitrary Lagrangian Eulerian method is applied to an existing finite element scheme. Some exact solutions to the shallow water equations in a parabolic basin are shown for comparison. An investigation is conducted into the accuracy of the method. I...

My long-term goal is to contribute, by means of an accurate hydrodynamics model, to efficient design, development and operation of autonomous underwater vehicles in energetic shallow waters. From a scientific viewpoint, the development of the AUV hydrodynamic model will contribute to a better understanding of wave-body-current interactions, nonlinear shallow-water waves, wave effects on stabili...

This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volumemethod. Numerical simulations show thatNEP is successful to be a refinement/coarsening indicator in the adaptive...

Periodic progressive waves in shallow to transitional water are described by a Cnoidal Approximation wave theory. The formulation is analytical and largely classical. Periodic waves are assumed, so that the theory does not extend to solitary waves. The solution is completed numerically, as a problem in nonlinear optimisation. The suitability of the theory in shallow to transitional water is dem...

Four new species of shallow-water marine gastropods belonging to the family Rissoidae are described from the Archipelago of the Azores: Setiaalexandrae sp. n., Setiaermelindoi sp. n., Setianetoae sp. n., and Manzoniamartinsi sp. n. These novelties increase the regional rissoid fauna to 39 species, of which 29 live in shallow-water habitats. A list of the species of Rissoidae from the Azores is ...

In this paper, a quasi-rogue wave solution of the Camassa-Holm equation is obtained by discrete method and Hirota’s bilinear transform method. The wave’s amplitude suddenly changes high and then suddenly disappears. The whole process experiences a very short time. Waveform’s characteristics are similar to rogue waves in shallow water. This obtained solution can be used to describe the possible ...

We derive a new completely integrable dispersive shallow water equation that is biHamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by using an asymptotic expansion directly in the Hamiltonian for Euler’s equations in the shallow water regime. The soliton solution for this equation has a limiting form that has a discontinuity in the f...