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, Kirby.
Detailed program and literature.

Course material and comments

  • First two weeks (Aug 9 and 16):
    • The keywords: 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
    • Here are the articles by Morhell & Pastoriza: 2013 , 2016
  • Third and fourth weeks (Aug 30 and Sep 6):
    • The keywords: Finite volume methods, Cell-centered schemes, Vertex-centered schemes, Numerical fluxes, Consistency, Convergence.
    • The main literature is Finite Volume Methods (Eymard et al, 2003), and Chapter 3 of Wesseling.
    • Here are the slides and exercises: Slides
    • It is recommended to watch the following video on the optimization of microchannels to minimize dispersion under electrokinetic-driven flow.
  • Fifth and sixth weeks (Sep 13 and Sep 20):
    • The keywords: Parallel viscous flow. Finite volumes in 2D. Vertex-centered and cell-centered FVs. Boundary conditions at walls. Time integration. Variable viscosity.
    • Here are the slides and exercises: Slides .
    • Finite volume code for fully developed flow: pipe_fd_t.m, ij2n.m, dpdz.m.
  • Seventh week (Sep 27):
  • Eighth week (Oct 04):
    • The keywords: Turbulence. Turbulence models.
    • Here are the slides and exercises: Slides .
  • Nineth week (Oct 11):
    • The keywords: Turbulence. Electro-osmotic particle steering.
    • Discussed the list of exercices on Turbulence. Introduced the concepts of electro-osmotic particle steerings and proposed the project.
  • Tenth week (Oct 18):
    • The keywords: Hyperbolic conservation laws in fluid mechanics.
    • Here are the slides and exercises: Slides .
  • Eleventh and twelfth weeks (Oct 25, Nov 1):
    • The keywords: Finite volume methods for hyperbolic linear systems. Extension to nonlinear problems.
    • Here are the slides and exercises: Slides .
    • Finite volume code for linearized shallow water flow: sw2016closed.m.
    • Finite volume codes for nonlinear shallow water flow mentioned in class: sw3.m, sw4.m.