Teaching

Numerical methods in hydraulic engineering - advanced course (2013)

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M. Jovanović (from top to bottom): vortex behind a cylindrical pier; deformation of the riverbed in the zone of pile groynes; kinetic energy of turbulence around physical models of a single simple groyne and a T-shaped groyne.

Postgraduate studies

ECTS credits: 8,5


Remark: This subject is parially lectured by three professors: M. Jovanović, M. Ivetić i R. Kapor. Below are presented contents of the part of the course lectured by M. Jovanović.

Lectures:


I. Elements of numerical analysis

  1. Numerical errors
  2. Numerical interpolation of functions
  3. Numerical approximation of functions
  4. Numerical differetiation
  5. Numerical integration
  6. Literature and appendixes

II. The Finite Element Method (FEM)

  1. General formulation of FEM
  2. Matrix formulation of FEM
  3. Calculation of the elementary matrices and vectors
  4. Numerical integration
  5. Assembling of the global matrix and the global vector
  6. An example from mathematics
  7. An example from hydraulics
  8. Literature and appendixes


III. Numerical modelling of waves with steep front
(Weak solutions for rapidly varying open-channel flows)

  1. 1. Governing equations (1D, 2D)
  2. The Riemann problem
  3. Conceptual approaches for problem solution
  4. Numerical models, example: the MacCormack numerical scheme
  5. Flux-splitting methods
  6. Methods of the Godunov class
  7. Literature

Literature:

  1. Carnahan, B., Luther, H.A., Wilkes, J.O., Applied Numerical Methods, Wiley, 1960.
  2. Ferziger, J.H., Numerical Methods for Engineering Application, Wiley, 1981.
  3. Hervouet, J-M., Hydrodynamics of Free Surface Flows, Wiley, 2007.
  4. Jovanović, M., Principles of num. modelling of 2D open-channel flows, F.Civ.Eng., 1998 (in Serbian).
  5. Pinder, G., Gray, W., Finite Element Simulation in Sruface and Subsurface Hydrology, Ac. Press, 1977.
  6. Press et al., Numerical Recipes, Cambridge University Press, 1986.
  7. Radojković, M., Klem, N., Computer application in hydraulics, Gradjevinska knjiga, 1989 (in Serbian).