Course detail

Mathematical models in hydrodynamic

FAST-CR51Acad. year: 2024/2025

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)

Entry knowledge

Mathematics, Hydraulics, Statics, Strain and stress analysis

Rules for evaluation and completion of the course

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

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.

Following knowledge:
1. 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.

Study aids

Not applicable.

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 literature

Not applicable.

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).