رسالة جامعية
Numerical methods for shallow water equations ; Αριθμητικές μέθοδοι για τις εξισώσεις ρηχών υδάτων
| العنوان: | Numerical methods for shallow water equations ; Αριθμητικές μέθοδοι για τις εξισώσεις ρηχών υδάτων |
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| المؤلفون: | Kounadis, Grigorios, Κουνάδης, Γρηγόριος |
| بيانات النشر: | National and Kapodistrian University of Athens Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ) |
| سنة النشر: | 2020 |
| المجموعة: | National Archive of PhD Theses (National Documentation Centre Greece) |
| مصطلحات موضوعية: | Εξισώσεις ρηχών υδάτων, Συστήματα boussinesq, Αριθμητικές μέθοδοι, Συνήθεις μέθοδοι Galerkin-πεπερασμένων στοιχείων, Ασυνεχείς μέθοδοι Galerkin (DG), Εκτιμήσεις σφαλμάτων, Απορροφητικές συνοριακές συνθήκες, Διάδοση διασπειρόμενων κυμάτων επιφανείας, Μοναχικά κύματα, Μεταβλητή τοπογραφία πυθμένα, Shallow water equations, Boussinesq systems, Numerical methods, Standard Galerkin finite element methods, Discontinuous Galerkin finite element methods, Error estimates, Characteristic boundary conditions, Surface dispersive long-wave propagation, Solitary waves, Variable bottom topography, Φυσικές Επιστήμες, Μαθηματικά, Natural Sciences, Mathematics |
| الوصف: | In the first chapter we state the Euler equations describing surface waves of an ideal fluid (water) in a two-dimensional waveguide of finite depth with variable bottom topography. The equations are written in nondimensional, scaled form using the scaling parameters ε=α₀/λ₀, μ=(D₀/λ₀)², where α₀ is a typical wave amplitude, λ₀ a typical wavelength, and D₀ an average bottom depth. From the Euler equations we derive a series of simple, approximate, models, that describe two-way propagation of nonlinear, dispersive surface waves in one dimension, that are long compared to the average bottom depth, i.e. satisfy μ≪1. The basic model are the Serre-Green-Naghdi (SGN) equations, from which three simpler mathematical models follow in specific regimes of scaling parameters: Α) the Classical Boussinesq system with variable bottom of general topography (CBs), in which ε=O(μ) and β=Ο(1), where β=B/D₀, with Β a typical bottom topography variation. B) the Classical Boussinesq system with weakly varying bottom, i.e. β=O(ε), (CBw). C) The system of shallow water equations (SW), where μ=0 and in general ε=O(1). The second chapter concerns the numerical analysis of initial and boundary value problems (ibvp’s) for the (CBs) and (CBw) systems in a finite interval with u=0 at the boundary. After a review of their theory of existence-uniqueness of solutions, the systems are discretized in space by the standard Galerkin-finite element method, and the semidiscretization error is estimated in L²×H¹. This estimate is verified by numerical experiments. We also examine Galerkin-FE methods for (CBw), (CBs), and (SW) with absorbing boundary conditions. Finally we study numerically, using mainly (CBs), changes that an initial solitary wave undergoes when moving into a region of variable bottom topography. In the third chapter we consider the (SW) with variable bottom, assuming smooth solutions. We prove error estimates in L²×L² for the standard Galerkin-FE semidiscretization for the ibvp with u=0 at the boundary, and with characteristic ... |
| نوع الوثيقة: | doctoral or postdoctoral thesis |
| اللغة: | English |
| العلاقة: | http://hdl.handle.net/10442/hedi/47680Test |
| DOI: | 10.12681/eadd/47680 |
| الإتاحة: | https://doi.org/10.12681/eadd/47680Test http://hdl.handle.net/10442/hedi/47680Test |
| رقم الانضمام: | edsbas.DCD5D285 |
| قاعدة البيانات: | BASE |
| DOI: | 10.12681/eadd/47680 |
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