TVM4155 - Numerical Models and Hydraulics


Examination arrangement

Examination arrangement: School exam
Grade: Letter grades

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours D

Course content

Analytical and numerical methods for computation of free surface profiles and flood waves in rivers. Metods to compute dispersion processes in 1, 2 and 3 dimensions. Algorithms to solve the Navier-Stokes equations for turbulent flow, including the use of computer programs. Topics from limnology, chemistry, biology and sediment transport, together with algorithms to model such processes in multiple dimensions.

Learning outcome


The student will get knowledge about:

  • How the following equations can be solved using a control-volume method: St. Venands equaiton, Convection-Diffusion equation and Navier-Stokes equations.
  • Quality of the solution of the equations: accuracy, stability and sources of errors.
  • Stratified flow, lake/reservoir hydraulics, discharge to receiving waters, sediment transport, turbulence models and models for water quality.


The student will know how to:

  • Use spreadsheets, HEC-RAS, SSIIM and OpenFOAM to compute stationary and non-stationary flow. - Make a grid for multi-dimensional numerical computations.
  • User simplified formulas for flood waves, discharge into receiving waters, dispersion of pollutants and sediment transport.

General competence

The student:

  • Know different computer programs for solutions of various flow problems.
  • Can assess the quality of the results from 1D, 2D and 3D numerical models and give specifications to quality tests.

Learning methods and activities

Lectures, assignments using computers and hand calculations. Lectures are given in English. 11 calculation exercises and 1 laboratory exercise.

Compulsory assignments

  • Exercises

Further on evaluation

Written school exam.

A minimum of 8 exercises must be approved in order to attend the exam.

Specific conditions

Admission to a programme of study is required:
Civil and Environmental Engineering (MTBYGG)
Hydropower Development (MSB1)

Required previous knowledge

Courses in Fluid Mechanics and Hydraulics

Course materials

"Numerical Modelling and Hydraulics", by N. Olsen. The book can be downloaded from our web pages: Additional selected scientific articles. Videos with lectures and assistance for homework.

Credit reductions

Course code Reduction From To
SIB5050 7.5
BM8700 7.5 AUTUMN 2023
More on the course

Version: 1
Credits:  7.5 SP
Study level: Second degree level


Term no.: 1
Teaching semester:  SPRING 2025

Language of instruction: English

Location: Trondheim

Subject area(s)
  • Hydraulic Engineering
  • Energy- and Environmental Physics
  • Hydraulic Engineering
  • Algorithm Construction
  • Numerical Mathematics
  • Analysis
  • Numerical Mathematics
  • Fluid Mechanics
  • Environmental Engineering
  • Hydro and Gas Dynamics
  • Hydraulics
  • Soil and Water Subjects
  • Technological subjects
Contact information
Course coordinator: Lecturer(s):

Department with academic responsibility
Department of Civil and Environmental Engineering


Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Spring ORD School exam 100/100 D INSPERA
Room Building Number of candidates
Summer UTS School exam 100/100 D INSPERA
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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