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Computational fluid mechanics 1


Part 1: Fluid Mechanics

  • Fluid physical properties
  • General conservation laws for viscous compressible Newtonian fluids
  • Dimensionless numbers (Reynolds, Mach …)
  • Viscous flows
  • Perfect fluid flows. Bernoulli theorem and its applications
  • Elementary boundary layer theory for laminar flows
  • Capillary effects


Tutorials: sound propagation, surface wave propagation, Magnus effect, Drag and Lift forces, pressure loss, Jurin law …


Part 2: Finite volume method

  • Mathematical study of first order scalar conservation laws: method of characteristics, weak solutions, Riemann problem, Kruskov theorem
  • Principles of the finite volume method
  • Explicit versus implicit schemes
  • Godunov scheme, Roe scheme …
  • Discrete maximum principle, TVD schemes, CFL condition


Labwork: Finite volume method applied to the solution of the traffic flow equation.


At the end of this module, the student should have understood the fundamental notions and principles of fluid mechanics and finite volume method:

  • Mass, Momentum and Energy conservation laws for fluids,
  • Compressible / incompressible, viscous / inviscid, laminar/ turbulent flows,
  • Boundary layer flows,
  • Dimensionless equations (Reynolds number, Mach number, Froude number, Bond number …)
  • Godunov and Roe finite volume schemes, TVD schemes.


The student will be able to:

  • Solve some fluid mechanics problem by using analytical methods
  • Compute orders of magnitude and predict qualitative behaviour of simple flows,
  • Use finite volumes schemes to solve non-linear scalar conservation laws

Needed prerequisite

Basis of general mechanics, continuum mechanics, numerical analysis and p.d.e. 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...