Course Details

Mathematical Modeling in Water Management

CR005 course is part of 1 study plan

Ing. full-t. program nC > V compulsory Winter Semester 2nd year 6 credits

Common bases for mathematical model creation. Modelling of water flow in water structures. Modelling of water flow in river network and floodplains. Reliability of water structures.

Course Guarantor

doc. Ing. Jan Jandora, Ph.D.


Institute of Water Structures

Learning outcomes

The result of the tuition is ability of students to deal with the problems of mathematical modelling in water management. After finishing the course, the student will be able:
- Explain the basic concepts of mathematical modeling
- Describe the basic equations of water flow - Navier-Stokes equations
- Explain the issue of turbulent flow
- Solve problems of water flow in 1D, 2D and 3D using analytical and numerical methods


Mathematics, Hydraulics, Hydrology, Soil Mechanics.



Planned educational activities and teaching methods

Course lectures are supplemented by presentations of mathematical and physical research on the faculty.

Forms and criteria of assessment

Successful conclusion of the course requires the completion of exercises with the granting of credit from the course, compliance with computing and conceptual part of the written test and the actual examination.


The aim of the course is to acquaint students with principles of mathematical modeling. The students will obtain knowledge about models of flow of water and water.

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.


2 hours/week, 13 weeks, elective

Syllabus of lectures

1st Introduction to problematic of mathematical modelling. Governing equations of fluid mechanics.
2 to 3 Modelling of turbulent flow.
4 to 5 Free surface flow (1D, 2D, hydraulic jump, sewer systems – aims, data, models).
6th Flow in pressure systems (aims, data, models).
7th Ground water flow problems (aims, data, models).
8th Modelling of advection and dispersion of matter – water quality in river networks and sewer systems (data, models, optimalization of WWTP costs).
9th Reliability of water structures (data, models).
10th Analytical and numerical solutions.


2 hours/week, 13 weeks, compulsory

Syllabus of practice

1st Introduction to problematic of mathematical modelling. Introduction to the software.
2 to 5 Modelling of ideal flow and laminar flow.
6 to 9 Modelling of turbulent flow.
10th Presentation of the results of modeling.