| Type: | Open University
Language: English |
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Prerequisite: 01030 Matematisk Analyse 3.04110 Numerisk Analyse.77256 Strømningslære/57105 Strømningsmekanik 2/10401Kontinuumsfysik
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Recommended semester: 7th - 9th semester
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Scope and form: Lectures and exercises
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Examination: Evaluation of report. (13-scale)
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Remarks: RELATED COURSES.
77371 Numerisk Fluid Mekanik
77566 Videregående Strømningslære
76271 Teoretisk Skibshydrodynamik I
76272 Teoretisk Skibshydrodynamik II
57221 Numerisk Hydrodynamik
57345 Bølgehydrodynamik
04202 Partielle differentialligninger
04225 Ikke-lineære partielle differentialligninger, solitoner
04310 Scientific Computing
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| Contact person: | Per Madsen, IMM, bygn. 305, tlf. 45253076 |
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Department: Informatics and Mathematical Modelling
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Aim: The course, consisting of lectures and problem sessions, will include theoretical and mathematical formulations and numerical methods with a view to compute nonlinear irregular water waves and their interaction with fixed and floating structures.
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Contents: With a starting point in the basic hydrodynamic equations, a number of mathematical and theoretical formulations for non-linear wave dynamics will be derived and analyzed. The lectures will concentrate on various levels of Boussinesq equations formulated in the time domain as well as the corresponding deterministic evolution equations in the frequency domain (Fourier-series with spatially varying oefficents). The analyses will concentrate on frequency-dispersion, amplitude-dispersion and non-linear transfer functions. Furthermore,
the lectures will introduce the concepts of stochastic evolution equations and bispectra.
Examples of numerical methods for the solution of the three- dimensional Euler equations and the two-dimensional Boussinesq equations will be given with emphasis on finite difference methods,
boundary integral methods and methods for handling moving boundaries (Marker-and-Cell, Volume-Of-Fluid, Level Set, Adaptive net).
The following physical phenomena will be treated in the course: Transformation of irregular waves over varying water depth; energy exchange between bound and free waves; generation and release of sub- and super-harmonic waves; low frequency waves in connection with surf beat and harbour resonance; wave breaking and generation of wave-driven currents; interaction between waves and currents including Doppler shift and wave blocking; interaction between waves and fixed/floating structures (e.g. moored ships).
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