Computational fluid dynamics

Nuclear Engineering, Second Cycle
1 ali 2 year
Hours per week – 1. semester:

Enrolment into the program.
Completed projects are necessary to enter the oral exam.

Content (Syllabus outline)

• Basic equations of fluid mechanics, heat transfer and mass transfer. Basic forms of equations. Models in fluid mechanics; classification of models depending on the type of leading partial differential equations.
• Review of basic numerical methods: finite difference, finite volume and finite element methods. Numerical methods for basic matrix operations. Parallelization.
• Euler equations of compressible flow. Numerical methods for solving systems of hyperbolic partial differential equations. Emphasis on explicit numerical schemes.
• Incompressible viscous fluid flow. Implicit and semi-implicit schemes. Solving the Poisson equation for the pressure field.
• Turbulence modelling: direct numerical simulation method, large eddy simulation (LES), Reynolds-averaged Navier–Stokes equations (RANS).
• Two-phase flow simulations.
Practical examples:
1. Development of own programs:

  • Solving 1D compressible flow hyperbolic equations
  • Solving equations of incompressible viscous flow in a simple geometry
  • Simulations using existing software packages:

  • Modelling of turbulent flow

  • Spectral schemes for direct numerical simulation of turbulence
  • Simple two-phase flow simulations
  1. Computational Fluid Dynamics: The Basics with Applications, John David Anderson, McGraw Hill, 1995
  2. Computational Methods for Fluid Dynamics, Joel H. Ferziger and Milovan Peric, Springer Verlag, 1999
  3. Computational Techniques for Fluid Dynamics, Specific Techniques for Differential Flow Categories, C. A. J. Fletcher, Springer-Verlag, 1991
Objectives and competences

Objectives: Acquire practical skills required to numerically solve the basic equations of fluid mechanics and heat and mass transfer. Development of their own software and use of existing software packages.
Competences: Modelling and ability to solve problems, computer skills.

Intended learning outcomes

Knowledge and understanding:
Knowledge of the basic partial differential equations of fluid mechanics and their solutions with finite differences / volumes - with student-made own and existing computer programs.
Understanding of other numerical methods used in fluid mechanics. Knowledge of basic turbulence models.
Solving basic equations of fluid mechanics and heat transfer using finite difference and finite volume methods. Use of existing software packages for simulation of concrete examples.
Along with basic mathematical models and numerical methods for their solution, the student is expected to critically asses the quality of the numerical solutions. These depend on the reliability of the mathematical model and the accuracy of the numerical scheme.
Transferable skills:
Basic conservation equations of fluid mechanics and heat transfer. Solving different types of ordinary and partial differential equations. Numerical methods: solving systems of linear and nonlinear equations, parallel programming.

Learning and teaching methods

Lectures, individual projects, consultations. Some content will be given in the form of e-lessons and with inclusion in current research projects.


grading of projects
oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Ivo Kljenak:
1. KLJENAK, I., MAVKO, B. Simulation of void fraction profile evolution in subcooled nucleate boiling flow in a vertical annulus using a bubble-tracking approach. Heat and Mass Transfer, 2006, vol. 42, pp. 552-561.
2. KLJENAK, I., BABIĆ, M., MAVKO, B., BAJSIĆ, I. Modeling of containment atmosphere mixing and stratification experiment using a CFD approach. Nuclear Engineering and Design, 2006, vol. 236, pp. 1682-1692.
3. BABIĆ, M., KLJENAK, I., MAVKO, B.. Simulations of TOSQAN containment spray tests with combined Eulerian CFD and droplet-tracking modelling. Nuclear Engineering and Design, 2009, vol. 239, no. 4, pp. 708-721.
Iztok Tiselj:
1. TISELJ, I, PETELIN, S. First and second order accurate schemes for two-fluid models. J. fluids eng., 1998, vol. 120 (2), str. 363-368.
2. TISELJ, I, ČERNE, G. Some comments on the behaviour of the RELAP5 numerical scheme at very small time steps. Nucl. sci. eng., 2000, 134, str. 306.
3. BERGANT R, TISELJ, I. Near-wall passive scalar transport at high Prandtl numbers. Phys. fluids, 2007, vol. 19, str. 065105-1 - 18.