Computational Fluid Dynamics
Gustavo Buscaglia
e-mail: gustavo.buscaglia at

Graduate course
1. Principles and equations of fluid mechanics.
2. Overview of numerical methods for fluid mechanics.
3. Fully-developed flow. Integral and differential formulations. Numerics.
4. A bit of turbulence.
5. Diffusion, convection and upwinding.
6. Incompressible Navier-Stokes equations and related models.
7. Discretization of the incompressible Navier-Stokes equations.
8. Hyperbolic conservation laws.
9. Finite volume methods for conservation laws.
10. Finite volume methods for nonlinear systems. Shallow water equations.
Texts: Wesseling, Leveque, Hirsch.
Detailed program and literature.

Course material and comments

  • First week (Aug 18):
    • The keywords of the week are: Continuous media, Conservation principles, Cauchy stress tensor, Action-reaction principle, Fluidity, Material derivative, Viscosity, Density.
    • Students who have no prior knowledge of Fluid Mechanics may want to read elementary material from books such as White.
    • Here are the slides and exercises: Slides
  • Second week (Aug 25):
    • Keywords of the week: Differential, integral and variational formulations. Discretization methods. Finite differences, finite volumes and finite elements.
    • Remember that we are setting up the web group.
    • Updated slides and exercises: Slides
  • Third week (Sep 1):
    • Keywords of the week: Parallel flows, fully developed flow. Conservation principles in parallel flow. Finite difference and finite volume discretization. Variable viscosity. Quasi-newtonian behavior. Viscous dissipation. Thermal effects.
    • Updated slides and exercises: Slides
    • Octave codes used in class: ij2n.m, pipe_fd_t.m, dpdz.m.
  • Fourth and fifth weeks (Sep 15 and 22):
    • Keywords of the weeks: Pipe flow. Turbulence. Reynolds average. Mixing length. Wall laws. The Navier-Stokes equations. Variants: Buoyancy-coupled flows. The k-epsilon turbulent model. Boundary conditions.
    • Updated slides and exercises: Slides
    • Reading material: Prosperetti_Chapter1, Prosperetti_Chapter2, Lew et al (2001).
  • Sixth and seventh weeks (Sep 29 and Oct 6):
  • Eighth week (Oct 13):
    • Keywords of the week: Conservation law. Differential and integral formulations. Hyperbolic conservation laws. Advection equation. Hyperbolic linear systems. Acoustics. Shallow water equations.
    • Updated slides and exercises: Slides
  • Nineth week (Oct 20):
    • Keywords of the week: Finite volume methods for conservation laws. Generalities. Lax-Friedrichs and Lax-Wendroff schemes for systems. Godunov scheme for systems.
    • Updated slides and exercises: Slides
    • Octave code used in class: sw2015a.m
  • Tenth week (Oct 27):
    • Keywords of the week: Boundary conditions for hyperbolic linear systems. Application to the linearized shallow water equations.
    • Octave code used in class: sw2015open.m, sw2015wave.m
  • Eleventh week (Nov 3):
    • Keywords of the week: Nonlinear conservation laws. Finite volume method for shallow water equations.
    • Updated slides and exercises: Slides

  • Oral presentations of course projects scheduled for December 1 and 8, 2015.