5 ECTS credits
125 u studietijd
Aanbieding 1 met studiegidsnummer 9017684ENR voor alle studenten in het 1e semester
met een verdiepend master niveau.
- Semester
- 1e semester
- Inschrijving onder examencontract
- Niet mogelijk
- Beoordelingsvoet
- Beoordeling (0 tot 20)
- 2e zittijd mogelijk
- Ja
- Onderwijstaal
- Engels
- Onder samenwerkingsakkoord
- Onder interuniversitair akkoord mbt. opleiding
- Faculteit
- Faculteit Ingenieurswetenschappen
- Verantwoordelijke vakgroep
- Hydrologie en Waterbouwkunde
- Externe partnerinstelling(en)
- KU Leuven
- Onderwijsteam
- Jaak MONBALIU
(titularis)
- Onderdelen en contacturen
- 26 contacturen Hoorcollege
32 contacturen Werkcolleges, practica en oefeningen
- Inhoud
- The aim of the course is to introduce advanced mathematical techniques for analyzing fluid mechanics and for obtaining practical solutions for fluid flow problems. The course covers a selection from each of the three topics given below.
1. Mathematical theory of fluid mechanics:
- Functions, vectors and tensors;
- Gradient, divergence and rotation operators; theorems of Green and Stokes; properties of irrotational, conservative and potential flow fields;
- Time derivatives; velocity and acceleration, material derivatives; particle paths, equipotential and streamlines; and
- Coordinate systems and transformation rules; Jacobian and Hessian matrices.
2. Partial differential equations for describing fluid dynamics:
- Characteristics and classification of differential equations;
- Properties of first order differential equations; solutions of kinematic wave equations and advection equations;
- Properties of 2nd order elliptic partial differential equations; Laplace and Poisson equations related to stationary flow problems; and
- Properties of 2nd order parabolic partial differential equations; diffusion problems, advection dispersion equations.
3. Numerical techniques:
- Numerical solution of systems of linear equations; relaxation techniques and conjugate gradient methods;
- Numerical solution of nonlinear equations, and systems of nonlinear equations;
- Numerical techniques for interpolation, differentiation and integration; and
- Least squares fitting and optimization techniques.
Practical:
- Exercises on functions and vector fields; calculation of potential functions and velocity fields, verification of conservation and rotation properties;
- Calculation of path lines and streamlines for simple fluid flow problems;
- Transformation of coordinate systems;
- Explicit and implicit numerical solutions for the advection-diffusion equation;
- Explicit and implicit numerical solutions for the momentum and continuity equations in 1 dimension;
- Solution of a kinematic wave equation problem, determination of wave velocities and mass transport velocities;
- Computer exercises on solutions of nonlinear problems;
- Computer exercises on interpolation, differentiation and integration of discrete data sets; andComputer exercises on curve fitting techniques.
- Studiemateriaal
- Digitaal cursusmateriaal (Vereist) : Text book, Toledo / e-platform
- Bijkomende info
- Text book
Toledo / e-platform
- Leerresultaten
-
Algemene competenties
- Become familiar with mathematical formulations in fluid flow problems;
- Become familiar with some elementary numerical techniques for solving fluid flow problems;
- Distinguish between ‘exact’ solution and numerical approximation; and
- Learn how to deal with different notations in different text books.Mathematical models are common place and are widely used by engineers dealing with water resources. Knowledge of and critical insight in analytical and numerical techniques is however essential not only when one wants to use these models, but also for understanding and evaluating their outcome.
- Beoordelingsinformatie
-
De beoordeling bestaat uit volgende opdrachtcategorieën:
Examen Andere bepaalt 100% van het eindcijfer
Binnen de categorie Examen Andere dient men volgende opdrachten af te werken:
- oral exam & quotation sample p
met een wegingsfactor 1
en aldus 100% van het totale eindcijfer.
Toelichting: Oral with written preparation. Quotation on sample problems and oral exam with written preparation.
- Aanvullende info mbt evaluatie
- oral with written preparation
Quotation on sample problems and oral exam with written preparation
- Toegestane onvoldoende
- Kijk in het aanvullend OER van je faculteit na of een toegestane onvoldoende mogelijk is voor dit opleidingsonderdeel.
Academische context
Dit studiedeel maakt geen deel uit van vastgelegde afstudeervereisten. Het is aldus een vrij keuzevak.