 # Modeling and scientific computing in fluid and structural mechanics

## Presentation

Programme (detailed contents) :

Brief review of the general concepts in continuum mechanics

Modeling and scientific computing in fluid mechanics :

• Dynamics of inviscid fluids
• Dynamics of Newtonian viscous fluids
• Capillary phenomena
• Numerical solution of fluid dynamics equations with the finite volume method (FVM)
• Implementation of the FVM to solve a model problem (dam break).

Modeling and scientific computing in structural mechanics

• Variational formulation and mathematical analysis of the elasticity problem
• Numerical resolution of elasticity with the finite element method
• Multiscale model and code coupling
• Application: modeling and computation of static as well as dynamic elastic problems through the use of an industrial software + development of python codes for the computation of stress concentration and local propagation of cracks within solids.

Organisation :

Conventional lectures/tutorials + class work (labwork)

Main difficulties for students :

• To connect their mathematical knowledge and the modelling issues to mechanics.
• To fully appreciate the finite volume and finite element methods for the numerical resolution of real physical problems.

## Objectives

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

The fundamentals of Mechanics for fluid and deformable solids, from a physical, mathematical and numerical point of view.

The student will be able to :

• Understand the physical meaning of the various terms used in fluid mechanics and elasticity models.
• Calculate exact solutions of simple problems and interpret them physically
• Evaluate orders of magnitude and know the physical meaning of the main dimensionless numbers
• Formulate and apply a finite volume method for numerically solving simple problems of fluid mechanics
• Formulate and solve the problem of elasticity by means of the finite element method.
• Use an industrial software to model and compute the elasticity problem in static as well as in dynamic.
• Write and implement a mixed formulation to couple different elastic domains and different numerical codes used as black-boxes.

## Needed prerequisite

Fundamentals in :

• Continuum mechanics
• Numerical analysis
• Partial derivative equations

## 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...

## Bibliography

G Duvaut, Mécanique des milieux continus, Masson, 2000, ISBN 2225816581

M Bonnet, A Frangi, Analyse des solides déformables par la méthode des éléments finis, Ecole Polytechnique , 2007, ISBN : 978-2-7302-1349-3

C. Hirsch, Numerical Computation of Internal and External Flows :

The Fundamentals of Computational Fluid Dynamic,  2007, Butterworth-Heinemann

Guyon, Hulin, Petit, Hydrodynamique Physique, 2012, EDP Sciences