Computational Fluid Mechanics I

Recommended Prerequisites

Fluid Mechanics and Introductory Numerical Methods.

Teaching Methods

Course lectures, in which the basic theory is covered using media (Slideshows, graphics and animations)  balanced with the resolution of some illustrative problems, will be complemented by computationally oriented laboratory sessions designed to give students experience with applications of the numerical methods. The main objective of the lab is to implement the numerical techniques developed in the course to problems of hydraulic engineering interest. The first part of this course will focus on review Fortan 90 programming language. At the end of each lab, a home assignment will be given. The assignment will involve a programming problem covering the key concepts of the particular module.

Learning Outcomes

This course is the first part of a two-semester sequence on Computational Fluids Mechanics. The two modules are devoted to an understanding of numerical techniques and their limitations, to use basic physical conservation principles to formulate problems and then solve them numerically. This first module will provide a solid foundation on traditional numerical discretization techniques and describes all the steps in the definition and development of a numerical simulation.
At the end of this first part, the students should be able to:
- Understand that conservation principles can be expressed in terms of differential equations that describe all relevant transport mechanisms, such as convection, diffusion, and dispersion.
- Know alternative spatial and time discretization methods for solving problems governed by the incompressible Navier-Stokes/Euler equations.
- Translate mathematical models into appropriate Fortran programs.
- Understand the basic principles of turbulence modeling approximations required to close RANS equations.

Work Placement(s)

No

Syllabus

- Governing equations of fluid flow.
- Common approximations and simplified equations.
- Introduction to the numerical modelling of fluid flow.
- Discretization approaches. Finite difference and finite volume methods. Introduction to Finite element method.
- Finite Difference Approximations. Consistency, stability and convergence.
- Mathematical nature of the fluid flow equations.
- The generic scalar transport equation. Pure convection and pure diffusion problems, convection-diffusion and wave equation. Water quality and groundwater modeling applications.
- Discretization schemes for the Incompressible Navier-Stokes equations.
- Introduction to numerical simulation of turbulent flows.

Head Lecturer(s)

José Manuel de Eça Guimarães de Abreu

Assessment Methods

Continuous
Exam: 50.0%
Work carried out during the semester: 50.0%

Bibliography

Ferziger J. H. and Periá M., Computational Methods for Fluid Dynamics , Springer-Verlag, 2002.

Hirsch C., Numerical Computation of Internal and external flows, Vol. II , 1989.

Versteeg, H.K. and Malalasekera, W., An introduction to Computational Fluid Dynamics: the Finite-Volume Method (2nd edition), Pearson, 2007.

White, F.M., Viscous fluid flow, McGraw-Hill, 1991.

Anderson, J., Computational Fluid Dynamics, McGraw-Hill, 1995.

Chapra, S. C. Surface water-quality modeling, WCB/McGraw-Hill, 1997.

Schlichting, H. and Gersten, K., Boundary layer theory, 8th Edition, Springer-Verlag,1999.
 
Pope, S.B., Turbulent flows, Cambridge University Press,  2000.

Wilcox, D.C., Turbulence modelling for CFD, 2nd Edition, DCW Industries, 1998.