Course detail

Mathematical modelling in water management

FAST-CR05Acad. year: 2013/2014

Common bases for mathematical model creation.
Modelling of water flow in water structures.
Modelling of water flow in river network and floodplains.
Modelling of water flow in sewer system and water supply network.
Ground water flow modelling.
Modelling of water quality in river network and sewer systems.
Reliability of water structures.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Jan Jandora, Ph.D.

Department

Institute of Water Structures (VST-VST)

Learning outcomes of the course unit

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

Prerequisites

Mathematics, Hydraulics, Hydrology, Soil Mechanics.

Co-requisites

Hydroinformatics.

Planned learning activities and teaching methods

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

Assesment methods and criteria linked to learning outcomes

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.

Course curriculum

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

Work placements

Not applicable.

Aims

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 education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

It is possible collaboration on research projects in the field of numerical modelling in water management.

Prerequisites and corequisites

Not applicable.

Basic literature

WILCOX, David C.: Turbulence Modeling for CFD. DCW Industries, Inc., 1994. ISBN 0-9636051-0-0. (EN)

Recommended reading

HAVLÍK, V., INGEDULD, P., VANĚČEK, S., ZEMAN, E.: Matematické modelování neustáleného proudění. ČVUT Praha, 1992. (CS)
CHUNG, T.J.: Computational Fluid Dynamics. Cambridge University Press, 2002. ISBN 0 521 59416 2. (EN)
ŘÍHA, Jaromír et al.: Matematické modelování hydrodynamických a disperzních jevů. PC-DIR Brno, 1997. ISBN 80-214-0827-8. (CS)

Classification of course in study plans

  • Programme N-K-C-SI Master's

    branch V , 2 year of study, winter semester, compulsory

  • Programme N-P-C-SI Master's

    branch V , 2 year of study, winter semester, compulsory

  • Programme N-P-E-SI Master's

    branch V , 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Jan Jandora, Ph.D.

Syllabus

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.

Exercise

26 hod., compulsory

Teacher / Lecturer

prof. Ing. Jan Jandora, Ph.D.

Syllabus

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.