Course Name
|
Turkish |
Gemi Hidrodinamiğinde Sınır Elemanları Yöntemleri
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| English |
Boundary Element Methods in Ship Hydrodynamics |
Course Code
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GEM 517E |
Credit |
Lecture
(hour/week) |
Recitation
(hour/week) |
Laboratory
(hour/week) |
| Semester |
-
|
3 |
3 |
- |
- |
| Course Language |
English |
| Course Coordinator |
Şakir Bal
Şakir Bal
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| Course Objectives |
The boundary element methods are one of very powerfull methods for the solution of complex probelms in ship hydrodynamics. It is mainly based on the discretization of boundaries of problem rather than the fluid domain itself. Some hydrodynamic singularities are distributed on the boundaries. The unknown strengths of corresponding singularities can be computed using kinematic boundary conditions. In this course, first, the basics of fluid mechanics are reviewed. Then, mathematical formulations and numerical implementations of boundary element methods are explained. The boundary element methods are applied to lots of ship hydrodynamics problems in homeworks and term projects. Students are expected to develop their own codes and algoritms as well as to use some commercial softwares.
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| Course Description |
Introduction, What are the boundary element methods?, Where do they apply?, Some of their advantages;
Review of fundamentals of Fluid mechanics, Velocity, pressure and shear stresses of fluid flow, Conservation of momentum equations, Constitutive relations - Navier-Stokes equations, Inviscid/irrotational flow - Velocity potential - Bernoulli's equation, Kinematic boundary condition, Lifting flows - Kutta condition;
Formulation of boundary element methods for Fluids, Green's theorem, The Green's source function, Green's identity - Integral equation for the potential on the boundary, The Neumann and Dirichlet boundary conditions, Velocity vs. potential formulations, Equivalence of the dipole and vorticity distributions;
Numerical implementation, Discretization of boundary into panels, Approximation of singularity distributions on the boundary, Galerkin vs. collocation approach, Matrix of influence coeffcients, Evaluation of infuence coeffients - The self-infuence coeffcient, Low-order (constant) vs. high-order (linear, quadratic) methods, Boundary shape discontinuities (corners), Hydrofoil trailing edge – Morino-Kutta condition, Error vs. number of panels and vs. computing time;
Applications, Flow about a 2-D non-lifting body, Flow about a 2-D lifting hydrofoil, Free-surfaces – Cavities, The dynamic boundary condition, Implementation of the dynamic boundary condition, Linear vs. non-linear approach, Vortex roll-up - Numerical stability, Unsteady flow problems - Convection of vorticity;
Other topics, Viscous/inviscid flow coupling, Hybrid BEM/FEM's methods, Stokes flows.
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| Course Outcomes |
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| Pre-requisite(s) |
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| Required Facilities |
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| Other |
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| Textbook |
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| Other References |
Brebbia and Dominguez , “Boundary Elements - An Introductory Course”,1991.
Breslin, J.P. ve Andersen, P., “Hydrodynamics of Ship Propellers”, Cambridge Univ. Press, 1994.
Faltinsen, O.M, “Hydrodynamics of High-Speed Marine Vehicles”, Cambridge University Press, 2005.
Katz, J. ve Plotkin, A., “Low Speed Aerodynamics from Wing Theory to Panel Methods”, McGraw-Hill Book Comp, USA, 2nd edition, 2001.
Kerwin, J. “Hydrofoils and Propellers”, MIT Ocean Engn., Lecture Notes, 2001.
Lamb, H., “Hydrodynamics”, 6th edition, Cambridge, Cambridge Univ. Press, 1963.
Moran, J, “An Introduction Theoretical and Computational Aerodynamics”, Wiley Inc.,
1984.
Newman, J.N., “Marine Hydrodynamics”, Cambridge, Mass., MIT Press, 1977.
Wrobel L.C. and Aliabadi M.H., “The Boundary Element Methods”, JohnWiley, 2002. |
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