Computational Fluid Dynamics
Gustavo Buscaglia and Fernando Mut.
e-mail: gustavo.buscaglia at and fermut 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.
4. Numerical approximation of steady and transient fully developed flows.
5. The convection-diffusion-reaction equation. Boundary and internal layers. Upwinding.
6. Mathematical formulations of the 3D incompressible Navier-Stokes equations.
7. MAC discretization. Monolithic and seggregated methods. Implementation.
8. Hyperbolic problems. Formulation and examples.
9. Hyperbolic schemes for linear systems. Linearized shallow water equations.
10. Hyperbolic schemes for nonlinear systems. Shallow water equations.
11. Turbulence. An overview.
Texts: Ferziger-Peric, Leveque, Hirsch.
Detailed program and literature.

Course material and comments

  • First week (Aug 13):
    • 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.
    • Read Chapters 1 and 3 of Buscaglia .
    • Read Chapters 1 and 2 of Nigro & Storti .
    • Read Lecture 3 of Bakker.
    • Read Chapter 1 of Hirsch.
    • Some questions that could help organize the concepts (in construction).

  • Second week (Aug 20):
    • The keywords of the week are: Discretization, Finite Differences, Order of Accuracy, Numerical Scheme, Explicit and Implicit Schemes, Truncation Error.
    • Read Lecture 1 of Bakker.
    • Read Chapter 2 of Ferziger & Peric.
    • Read Chapter 2 of Hirsch.
    • Watch Lectures 1, 2 and 3 of Lorena Barba (read me!).

  • Third week (Aug 27):
    • The keywords of the week are: Fully developed flow. Balance of mass and forces in simple control volumes (small cube, annulus). Force on a rectangular surface aligned with the axes. Friction factor. See the posting at the Google Group.
    • Next week classes will be Monday thru Friday, at 9 am (until noon). Next Monday come to Prof. Buscaglia's office (4-219 at ICMC) at 8.45 am, from there we all go to the classroom.

  • Fourth week (Sep 2-6):

  • Fifth week (Sep 9-13):

  • Sixth week (Sep 16-20):

  • Eighth week (Sep 30 - Oct 4):
    • The keywords of the week are: Navier-Stokes equations. Interpretation of each term. Balance of mass and momentum in a control volume. Strain rate. Vorticity. Stream function. Compressibility and Incompressibility.
    • Our goal is to understand the Navier-Stokes equations in general, and then focus specifically on the incompressible case. We consider the differential and integral conservation laws, and the physical or mathematical boundary conditions that can be imposed. As discussed in the classroom, we must understand derived quantities such as shear stress, dissipation rate, pressure loss, flow rate, etc.
    • This week we concentrate on reading Chapter 12 of Hirsch Lectures 4, 5, 6 and 7 of Bakker. We do not get very technical. The precise details will be discussed next week, when we will discuss a specific approximation method.

  • Ninth week (Oct 7 - 11):
    • The keywords of the week are: Navier-Stokes equations. Marker and Cell discretization. Implementation. Pressure Poisson equation.
    • Our goal is to code a MAC 2D solver and run on a benchmark case.
    • This week we concentrate on reading Chapter 2 of the book by Prosperetti and Tryggvason.
    • Also for this week is the beginning of our Course Project. It begins with the second Mini-Project which is mandatory for all students. The project is to code (in Octave) the method proposed in the chapter we are reading. The goal is to compute the steady state velocity and pressure fields in the flow over a 1:2 expansion as described in the attached document. All students have to code the MAC method for the transient Navier-Stokes equations and solve until reaching the steady state, and report velocity and pressure profiles at specific locations. Most of the students will use this program for the Course Project itself, though not all.
    • The deadline for a two-page report on this miniproject is October 22!! (two weeks! start today!)
    • Quadros de outro ano que podem servir: 1, 2.

  • Tenth week (Oct 14 - 18):
    • The keywords of the week are: Conservation laws. Hyperbolic equations and systems. Rankine-Hugoniot conditions. Traffic flow. Burgers' equation. Acoustic equations.
    • This week we concentrate on reading Chapters 1, 2 (except for 2.12-2.14) and 11 of LeVeque's book "Finite-volume methods for hyperbolic problems" and Chapters 1 to 5 of LeVeque's book "Numerical methods for conservation laws". We will have a talk about this topic in the classroom, but you must try to understand it by yourself.
    • We of course keep on coding, since deadline for Miniproject 2 is next Tuesday.

  • Eleventh week (Oct 21 - 25):
    • This week we keep on coding for Miniproject 2, finish the report, and gather forces for next week "on campus" sessions.

  • Twelfth week (Oct 28 - Nov 1):
    • This week we meet at ICMC for intensive learning activities, mainly focused on the numerical solution of hyperbolic systems and of the incompressible Navier-Stokes equations.
    • Some blackboard pictures that will be used in the classroom: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.
    • Some blackboard pictures of this year: 1, 2.
    • The Octave codes for hyperbolic equations used in the classroom: traffic.m, sw3.m, sw4.m.
    • The Octave codes for Navier-Stokes (MAC) used in the classroom: ij2n.m, ij2nu.m, ij2nv.m, ns_mac_abcn.m, ns_mac_vortex.m, ns_mac.m, parabola.m.

  • Last month (November 2013):
    • This month you are supposed to work on your project. The list of projects can be found here.