Course detail

Mathematical models in hydrodynamic

FAST-CR51Acad. year: 2013/2014

Introduction to mathematical modelling of hydrodynamic processes (classification of hydrodynamic tasks, initial and boundary problems)
Governing equations of fluid mechanics (conservation laws, momentum law, equations of state)
Laminar and turbulent flow (mathematical formulation, Navier-Stokes equations, turbulent modelling)
Shallow water flow modelling (mathematical formulation, applied turbulent models)
1D free surface flow modelling (mathematical formulation, flow in sewer systems, open channel flow)
Pressure systems flow in 1D (mathematical formulation, models of steady pressure flow in pipe systems)
Modelling of advection and dispersion of matter (mathematical formulation, steady and unsteady models)
Static of water structures (plane stress, plane deformation)
Direct and indirect modelling (direct and inverse problems)

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Jaromír Říha, CSc.

Department

Institute of Water Structures (VST-VST)

Learning outcomes of the course unit

The result is the ability of graduate to classify hydrodynamical problems in terms of mathematical modelling, to demonstrate approaches at deriving governing equations in fluid mechanics (mass and energy balance, momentum conservation, equations of state) and to specify boundary and initial conditions. The course deals with laminar and turbulent modelling, open channel and floodplain hydraulics and groundwater flow.

Prerequisites

Mathematics, Hydraulics, Statics, Strain and stress analysis

Co-requisites

Numerical methods, statistics

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. The seminars are held in computer laboratory.

Assesment methods and criteria linked to learning outcomes

100% presence in seminars, exceptionally 2 seminars - apologized, for exam the credit is necessary, for positive evaluation at least partial knowledge in each of 3 questions

Course curriculum

1. Introduction (classification of problems, initial and boundary problems)
2-3. Conservation laws, momentum equation, equations of state
4-5. Derivation of governing equation for simplifying assumptions (1D, 2D, steady state)
6. Laminar and turbulent flow
7. Shallow water equation
8. Free surface flow problems
9. Problems of water flow in pressure systems
10-11. Advection and dispersion of matter in water
12. Sediment load transport, dam breaking caused by overtoping
13. Modelling stability of hydro technical structures. Direct and inverse modelling.

Work placements

Not available

Aims

The aim is to classify hydrodynamical problems in terms of mathematical modelling, to demonstrate approaches at deriving governing equations in fluid mechanics (mass and energy balance, momentum conservation, equations of state) and to specify boundary and initial conditions. The course deals with laminar and turbulent modelling, open channel and floodplain hydraulics and groundwater flow.

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

Participation at the research projects of the Institute.

Prerequisites and corequisites

Not applicable.

Basic literature

Bear, J. - Verruijt, V.: Modelling Groundwater Flow and Pollution. Elsevier, Amsterdam, 1987. (EN)
Havlík, Ingeduld, Vaněček, Zeman: Matematické modelování neustáleného proudění. ČVUT Praha, 1992. (CS)
Říha a kol.: Matematické modelování hydrodynamických a disperzních jevů. PCDIR Brno, 1997. (CS)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme N-K-C-SI Master's

    branch V , 1 year of study, summer semester, elective

  • Programme N-P-C-SI Master's

    branch V , 1 year of study, summer semester, elective

  • Programme N-P-E-SI Master's

    branch V , 1 year of study, summer semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Jaromír Říha, CSc.

Syllabus

1. Introduction (classification of problems, initial and boundary problems)
2-3. Conservation laws, momentum equation, equations of state
4-5. Derivation of governing equation for simplifying assumptions (1D, 2D, steady state)
6. Laminar and turbulent flow
7. Shallow water equation
8. Free surface flow problems
9. Problems of water flow in pressure systems
10-11. Advection and dispersion of matter in water
12. Sediment load transport, dam breaking caused by overtopping
13. Modelling stability of hydro technical structures. Direct and inverse modelling.

Exercise

26 hod., compulsory

Teacher / Lecturer

prof. Ing. Jaromír Říha, CSc.

Syllabus

1. - 2. Introduction to ANSYS code
3. - 5. Stress and strain analysis of hydrstructures
6.-7. Unsteady pressure groundwater flow
8. Groundwater flow - problems with phreatic surface.
9. - 10. Dam breaching due to piping and overtopping.
11. - 13. Water quality modelling (dynamic, balance).