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, 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, 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
 Here are the articles by Morhell & Pastoriza: 2013 , 2016

Third and fourth weeks (Aug 30 and Sep 6):
 The keywords: Finite volume methods, Cellcentered schemes, Vertexcentered 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 electrokineticdriven flow.

Fifth and sixth weeks (Sep 13 and Sep 20):
 The keywords: Parallel viscous flow. Finite volumes in 2D. Vertexcentered and cellcentered 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):
 The keywords: Incompressible NavierStokes equations. MAC discretization. Boundary conditions. Monolithic and projection schemes. ABCN time discretization.
 Here are the slides and exercises:
Slides .
 Finite volume code for Stokes flow, monolithic: codemac.m, ij2ng.m.
 Finite volume code for NavierStokes flow, ABCN projection: ns_mac_abcn.m, ij2n.m, ij2nu.m, ij2nv.m, parabola.m.
 Reading material: ProsperettiTryggvasson, chapter 2.
 Reading material for next week: Bakker Lecture 8, Bakker Lecture 9, Bakker Lecture 10, Iaccarino Lecture, Mc Donough Lectures (first 100 pages)..

Eighth week (Oct 04):
 The keywords: Turbulence. Turbulence models.
 Here are the slides and exercises:
Slides .

Nineth week (Oct 11):
 The keywords: Turbulence. Electroosmotic particle steering.
 Discussed the list of exercices on Turbulence. Introduced the
concepts of electroosmotic 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.