5 ECTS credits
125 h study time
Offer 1 with catalog number 9017684ENR for all students in the 1st semester
at
a (E) Master - advanced level.
- Semester
- 1st semester
- Enrollment based on exam contract
- Impossible
- Grading method
- Grading (scale from 0 to 20)
- Can retake in second session
- Yes
- Taught in
- English
- Partnership Agreement
- Under interuniversity agreement for degree program
- Faculty
- Faculty of Engineering
- Department
- Hydrology and Hydraulic Engineering
- External partners
- KU Leuven
- Educational team
- Jaak MONBALIU
(course titular)
- Activities and contact hours
- 26 contact hours Lecture
32 contact hours Seminar, Exercises or Practicals
- Course Content
- 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.
- Course material
- Digital course material (Required) : Text book - Toledo / e-platform, Toledo / e-platform
- Additional info
- Text book
Toledo / e-platform
- Learning Outcomes
-
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.
- Grading
-
The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.
Within the Other Exam category, the following assignments need to be completed:
- oral exam & quotation sample p
with a relative weight of 1
which comprises 100% of the final mark.
Note: Oral with written preparation. Quotation of sample problems and oral exam with written preparation.
- Additional info regarding evaluation
- oral with written preparation
Quotation on sample problems and oral exam with written preparation
- Allowed unsatisfactory mark
- The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.
Academic context
This course offer isn't part of a fixed set of graduation requirements. Hence, it is a free elective.