Mathematical modelling in hydraulic research

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Code Completion Credits Range Language
D42MMH ZK 1P+1C Czech
Garant předmětu:
Petr Valenta
Petr Valenta
Petr Valenta
Department of Hydraulic Structures

The course focuses on numerical modelling of free surface water flow and its application in practical hydraulic problems of river hydraulics. In terms of dimensionality, it focuses mainly on the problems of one-dimensional and two-dimensional modelling. The theoretical part of the course is devoted to the general possibilities of investigating flow characteristics, mathematical description of flow, classification of numerical models of water flow with a focus on the mathematical formulation of the initial system of governing equations, approaches to turbulence modelling, spatial schematisation, discretization and numerical solution of the problem using the most used methods of solving governing equations (finite difference method, finite element method, finite volume method). On a practical level, the course covers the conditions for practical application of models, requirements for input data and their accuracy, including the use of modern remote sensing data, specification of boundary conditions, calibration of models, and methods of evaluating results and presenting outputs.


The interrelationship between the student's study focus and the anticipated content of his/her dissertation and the content of the course. Knowledge from previous studies (mathematics, hydraulics).

Syllabus of lectures:

Seminars and consultations in the following areas:

Objectives and means of numerical water modelling

Dimensionality of numerical models

Mathematical description of water flow in river channels

The governing equations of numerical models of water flow

Turbulence models

Methods of discretization and solution of governing equations

Boundary and initial conditions

Input data for modelling including remote sensing data

Calibration of models

Postprocessing - processing, evaluation and application of modelling results

Syllabus of tutorials:

Elaboration of professional research according to the specific focus of the student and according to the agreement with the lecturer

Study Objective:

Introduction to the theoretical foundations and practical application of numerical modelling in hydrotechnical research in the field of river hydraulics

Study materials:

•TU, J., YEOH, G. H., LIU, CH. : Computational Fluid Dynamics - A Practical Approach. Elsevier, ©2008, 459 s. ISBN 978-0-7506-8563-4.

•CUNGE, J. A., HOLLY F. M., VERWEY, A.: Practical Aspects of Computational River Hydraulics. Pitman Publishing, ©1980, 420 s., ISBN 0-273-08442-9.

•PATANKAR, S.: Numerical Heat Transfer and Fluid Flow. McGraw-Hill, ©1980.

•GRAF, W.H. ALTINAKAR, M. S.: Fluvial Hydraulics. John Wiley & Sons, ©1998. 681 s. ISBN 0-97714-4.

•PINDER, F., GRAY, W.G. : Finite Element Simulation in Surface and Subsurface Hydrology. Academic Press, ©1977, 295 s. ISBN 0-12-556950-5.

Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-04-17
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