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C2. MATHEMATICS FOR WATER ENGINEERING
(KUL-code: HF38 (Th); HF39 (Pr))
Lecturer: MONBALIU J.
ECTS-credit: 5 pts
Contact hours: 30 hrs. of theory/30 hrs. of practical
Prerequisites: Basic knowledge of calculus, matrix algebra and numerical methods; use of a
spreadsheet
Time and place: 1st semester, 13 sessions of 3 hours each, K.U.Leuven
Course syllabus: Lecture notes
Evaluation: Quotation on sample problems and oral exam with written preparation
Comparable handbook: C.R. Wylie & L.C. Barret. Advanced engineering mathematics. Mc Graw-Hill
K. Arbenz & A. Wohlhauser. Advanced mathematics for practicing engineers. Artech
House
Lecture notes on computational hydraulics
Additional information: Emphasis is on exercises (hand-on experience); many exercises need to be solved on
computer (spreadsheet); students are introduced to the matlab software package for the
solution of certain problems.
Learning objectives:
- 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
- learn how to deal with different notations in different text books
Mathematical models are commonplace 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.
Course description:
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;
- 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.
The practical work consists of a selection from:
5 / Course syllabi