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Modeling and scientific computing in fluid and structural mechanics


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.


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...


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