Graduate Course on Computational Fluid Dynamics

Computational Fluid Dynamics

Professor

Gustavo Buscaglia

e-mail: gustavo.buscaglia at gmail.com

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):

Keywords of the weeks: Marker-and-Cell discretization of the Navier-Stokes equations as a finite volume method. Adams-Bashforth Crank-Nicolson scheme. Monolithic and projection strategies. Revision of previous material.
Updated slides and exercises: Slides
Reading material: Sousa et al (2015), Prosperetti_Chapter2. Chapter 7 of Wesseling.
Octave codes used in class: ij2n.m, ij2nu.m, ij2nv.m, ns_mac_abcn.m, parabola.m. Notice that this code is defined so as to solve this problem.
The projects for group work are here.

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.