A Hamiltonian coupled mode method for the fully nonlinear water wave problem, including the case of a moving seabed

Χαραλαμπόπουλος, Αλέξης-Τζιάννι; Charalampopoulos, Alexis-Tzianni

dc.contributor.author	Χαραλαμπόπουλος, Αλέξης-Τζιάννι	el
dc.contributor.author	Charalampopoulos, Alexis-Tzianni	en
dc.date.accessioned	2016-12-19T12:44:07Z
dc.date.available	2016-12-19T12:44:07Z
dc.date.issued	2016-12-19
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/44170
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.13568
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/gr/	*
dc.subject	Water waves	en
dc.subject	Calculus of variations	en
dc.title	A Hamiltonian coupled mode method for the fully nonlinear water wave problem, including the case of a moving seabed	en
heal.type	bachelorThesis
heal.classification	Μη γραμμιικά κύματα ελεύθερης επιφάνειας	el
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2016-10-06
heal.abstract	Over the last few decades, the study of water waves is becoming relevant for more applications, surpassing their traditional study regarding ships and coastal structures and engulfing relatively new fields such as offshore platforms and energy harvesting from water waves. These problems are usually defined over very large physical domains and hence, the classic and fully nonlinear Navier-Stokes equations have found limited applicability due to their complexity and vast demand of computational time. Hence, the nonlinear irrotational (and inviscid) water wave problem (NLIWW) has been greatly employed for the study of many practical and highly demanding cases, with many new numerical methods arising. The framework of said new methods is the strive for computationally efficient solvers for highly nonlinear and complex problems. In the first Chapter of this thesis, we present and describe the Hamiltonian Coupled-Mode method (HCM) for the full NLIWW problem. This method was first presented for the fully nonlinear problem in (Athanassoulis & Belibassakis, 2000). For this purpose we utilize an exact vertical eigenfuction series expansion together with Luke’s unconstrained variational principle to derive an equivalent variational reformulation of the NLIWW problem. Concerns regarding the validity of this reformulation, which were initially presented in (Athanassoulis et al., 2016), are also addressed. We then proceed to reformulate the Euler-Lagrange equations by using a more computationally efficient system as was presented in (Athanassoulis & Papoutsellis, 2015). In the second Chapter, we calculate analytically the coefficients of the new formulation and present a way their computation can be implemented efficiently. We also present asymptotic results regarding these coefficients and other components of the model. Finally, we describe the truncated system to be used for the numerical implementation and, although we do not prove formally the validity of this truncation, we state some arguments in favor of its usage. For the numerical part, in Chapter 3, we develop an efficient and parallel implementation of the model utilizing C++. The code can use an arbitrary order for the finite difference method (FDM) with results being presented for schemes from 2nd order up to 12th order. We also analyze the form the discretized system assumes. We then describe the 4th order classical Runge-Kutta method used for the numerical time integration of the solution, completing thus the description of the code. To prove its numerical accuracy and efficiency the code is tested with computationally demanding, highly nonlinear cases. At first the accurate and efficient calculation of the DtN operator is of great importance and a variety of results regarding that matter are presented for a commonly used analytical test case. Following that, we verify the ability of the code to model a variety of complex problems, starting from long-time propagation of solitary waves, reflection of solitary waves on a vertical wall and asymmetric collision of two solitary waves over a flat bottom. We then proceed to present results for seabeds of arbitrary (and quite abrupt) bathymetry with solitary waves propagating over them. Finally, we address the problem of a moving seabed by simulating and presenting results for the experiments executed by Hammack in (Hammack, 1973).	el
heal.advisorName	Αθανασούλης, Γεράσιμος	el
heal.committeeMemberName	Τριανταφύλλου, Γεώργιος	el
heal.committeeMemberName	Μπελιμπασάκης, Κωνσταντίνος	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Ναυπηγών Μηχανολόγων Μηχανικών. Τομέας Ναυτικής και Θαλάσσιας Υδροδυναμικής	el
heal.academicPublisherID	ntua
heal.numberOfPages	197 σ.
heal.fullTextAvailability	true