HWM-33806 Water and Air Flow Numerical Techniques


Credits 6.00

Teaching methodContact hours
Course coordinator(s)MSc PhD LA Melsen
Lecturer(s)ing. G Bier
MSc PhD LA Melsen
dr. ir. CC van Heerwaarden
Examiner(s)ing. G Bier
dr. ir. CC van Heerwaarden
MSc PhD LA Melsen

Language of instruction:


Assumed knowledge on:

Water Quantity and Quality (SLM-20806) or Meteorology and Climate (MAQ-21806) or a similar background in hydrology and/or meteorology. Assumed background in mathematics: MAT-23306 Multivariate Mathematics Applied (or comparable).

Continuation courses:

MAQ-31806 Atmospheric Modeling;
SLM-33306 Advanced Hydrological Systems Analysis.


This course introduces numerical techniques for stationary and dynamical flow in the context of hydrology and the atmospheric sciences. Flow problems for a special class of differential equations as the description of the states involves both storages and vector fields of flows. Solution domains and boundary conditions should be defined in terms of these. Numerical techniques such as finite differences, finite volumes, and finite elements, which are especially suited for this type of problems, will be discussed. The last topic covered is sensitivity analysis, which deals with the evaluation of the implemented models.

Learning outcomes:

After successful completion of this course students are expected to be able to:
- explain the concepts and basics of three different numerical techniques to solve flow problems;
- conduct simple manual calculations based on the three different numerical techniques;
- able to implement and/or apply numerical techniques in scripting language;
- know how to implement different types of boundary conditions;
- know the steps and requirements of setting up a spatial model;
- explain the theory and concepts of two sensitivity analysis methods;
- conduct a sensitivity analysis on model parameters;
- critically analyse and appraise results from numerical models.


- classroom lectures;
- computer assignments using R;
- discussion of assignments.


Marks are based on a written examination (70%) and a final assignment (30%). A minimum grade of 5.5 for the written examination, and a minimum grade of 5.5 overall (0.7*mark written examination + 0.3*mark final assignment) is required to pass. 


Lecture slides and practical assignments, shared through Brightspace.

Compulsory for: MEEEarth and EnvironmentMScA: Spec. A - Hydrology and Water Resources3WD
Restricted Optional for: MEEEarth and EnvironmentMScB: Spec. B - Meteorology and Air Quality3WD
MCLClimate StudiesMScA: Spec. A - The Physical Climate System3WD