 # Advanced models and numerical methods for fluid mechanics

## Presentation

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.

## Objectives

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...