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Advanced models and numerical methods for fluid mechanics


Programme (detailed contents) :


Compressible Flow Modelling (13h45) :


- Models for compressible fluid dynamics. Discontinuous solutions and Rankine Hugoniot relationships. Riemann's problem. Application examples in the field of high speed flows.

- Finite Volume schemes of order 1 and 2. MUSCL method. Lab work

- High order numerical methods. Lab work


Two-phase flow modelling (8h)


- Models for two-phase flows. Application examples in the industrial and environmental fields.

- Numerical methods for two-phase flows.

- Lab work on the VOF method.


Modeling of turbulent flows (13h15)


- Models for turbulent flows (k-epsilon, k-omega, L.E.S, wall laws) and application examples.

- Lab work on the modelling of turbulent boundary layers



Organisation :


Conventional lectures/tutorials + class work (labwork)


Main difficulties for students :


Balance between mathematical rigour and the level of approximation necessary to obtain physical models adapted to the desired level of description.


At the end of this module, the student will have understood and be able to explain (main concepts) :


  • the different models used to describe the dynamics of turbulent flows, compressible flows and two-phase flows;
  • the main numerical methods used in computational fluid mechanics: finite volume method (order 1 and 2), VOF method, high order methods (DG, SD ...).


This course completes and deepens the basic notions of the S8 course entitled: "Numerical models and methods for fluid and structural mechanics".


The student will be able to :

  • Understand the models used to describe the dynamics of compressible flows (with possible presence of shock waves), two-phase flows and turbulent flows,
  • Know the underlying assumptions and the limits of validity of these models,
  • Know/understand the main numerical methods used in CFD and apply them, 
  • Use a model and a numerical method adapted to the fluid mechanics problem to be solved and the desired accuracy.

Needed prerequisite

Basic skills in computational fluid mechanics (dynamics of incompressible flows, general principles of the finite volume method)

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...