Computational Fluid Dynamics
 Professor
 Gustavo Buscaglia
 email: gustavo.buscaglia at
gmail.com
 Graduate course

1. Principles and equations of fluid mechanics.
2. Overview of numerical methods for fluid mechanics.
3. Fullydeveloped flow. Integral and differential formulations. Numerics.
4. A bit of turbulence.
5. Diffusion, convection and upwinding.
6. Incompressible NavierStokes equations and related models.
7. Discretization of the incompressible NavierStokes 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, Actionreaction 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. Quasinewtonian 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 NavierStokes equations. Variants: Buoyancycoupled flows. The kepsilon 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: MarkerandCell discretization of the NavierStokes equations as a finite volume method. AdamsBashforth CrankNicolson 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. LaxFriedrichs and LaxWendroff 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.