Study Programmes 2015-2016
AERO0030-1  
Computational fluid dynamics
Duration :
30h Th, 20h Pr, 10h Labo.
Number of credits :
Master in aerospace engineering (120 ECTS)5
Master in physical engineering (120 ECTS)5
Master in physical engineering (120 ECTS)5
Lecturer :
Vincent Terrapon
Language(s) of instruction :
English language
Organisation and examination :
Teaching in the second semester
Units courses prerequisite and corequisite :
Prerequisite or corequisite units are presented within each program
Course contents :
Computational fluid dynamics (CFD) consists in solving numerically the equations governing the motion of fluids. In other words, CFD relies on advanced numerical methods and algorithms to predict complex flows. CFD has seen a rapid and continuous development in the past decades and has now established itself as an essential tool in the design of engineering applications (e.g., optimization of aircraft aerodynamics) and the analysis and prediction of natural systems (e.g., weather prediction). This rapid development is directly linked with the steadily increase in computing power. Because of the prevalence of complex fluid flows in engineering and natural systems, CFD has become an indispensable tool in engineering.
This course is an introduction into CFD. It thus focuses on the classical aspects of numerical analysis and does not intend to describe all possible methods and more advanced algorithms. The material covered follows very closely the mandatory textbook. Additional details are added to some parts to complement the textbook.
The following topics are covered:
  • Introduction (role of CFD, methodology, limitations)
  • Basic equations of fluid mechanics (conservation laws, incompressibility, moving control volumes)
  • Levels of approximations to the basic equations (Navier-Stokes equations, DNS, LES, RANS, boundary layer approximation, inviscid flows)
  • Mathematical nature of the flow equations and boundary conditions (convection-diffusion equation, partial differential equation of second order, hyperbolic/ parabolic/ elliptic equations, conservation form of the equations)
  • Finite difference method on structured grids (order of derivatives, order of accuracy, multi-dimensional space, non-uniform grids, centered and skewed stencils, implicit formulas)
  • Finite volume and finite element methods (conservative discretization, general formulation, practical implementation, estimation of gradients, weak formulation, weighted residuals, Galerkin method)
  • Structured and unstructured grid properties (non-uniform, body-fitted, multi-block, tetrahedral and hexahydral, hybrid, evaluation of cell areas and volumes, best practice)
  • Consistency, stability and error analysis (definitions, von Neumann stability analysis, new schemes for convection, spectral analysis of numerical errors, numerical oscillations)
  • General properties and high-resolution numerical schemes (two-level schemes, stability issues, generation of new schemes, monotonicity, Godunov's theorem, limiters)
  • Time integration methods for space-discretized equations (matrix representation of operators, eigenvalue spectrum, Fourier modes, stability regions, implicit and explicit schemes, predictor-corrector schemes, ADI method)
  • Iterative methods for the resolution of algebraic systems (point Jacobi and Gauss-Seidel, convergence analysis, overrelaxation, preconditioning, multigrid method)
  • Numerical simulation of inviscid flows (influence of compressibility, discontinuities, space discretization, time integration, boundary conditions)
  • Numerical solutions of viscous laminar flows (boundary conditions, grid, density-based methods, pressure correction methods, best practice)
Learning outcomes of the course :
At the end of the course, the students should be able to:
  • Apply the complete methodology of a CFD analysis
  • Set up a simulation with an appropriate numerical method, correct boundary conditions, adequate initial conditions, and adequate parameter values
  • Understand the basic options of a commercial or open source CFD software and their corresponding impact on the numerical solution
  • Understand the close link between the physics, the equations and the numerical schemes
  • Be able to assess a numerical scheme based on stability, consistency and accuracy considerations
  • Know the major numerical schemes, their domain of applicability, and their advantages and shortcomings
  • Differentiate between methods for incompressible and compressible flows
  • Simulate a simple flow with a commercial or open source CFD code
  • Critically assess CFD results
Prerequisite knowledge and skills :
To efficiently follow this course, it is preferable to have some basic knowledge in fluid mechanics (conservation principles, Navier-Stokes equations, dimensional analysis, ...), in numerical analysis and in basic mathematics.
Planned learning activities and teaching methods :
The formal class takes place each week for about 2 hours. It focuses on the theoretical concepts that are additionally illustrated by numerous examples.  Additionally, students are expected to regularly read the accompanying textbook to consolidate this theory and gain a more in-depth understanding of some of the details omitted in class.
Homework problems are also distributed every week. Students are expected to work on them individually. These problem sets consist in solving analytical exercises or developing small programs in Matlab. They illustrate the concepts seen in class and help consolidate the material. They are also a very good preparation for the final exam. Homework problems are not graded and are not directly discussed in class, but students are encouraged to contact the assistant or the instructor if they have any question. 
Additionally, four tutorials are organized after the formal lecture. Their objective is to illustrate the theoretical concepts seen in class in real case examples. These tutorials are based on OpenFOAM  concrete simulation examples and take place in the computer room. 
Mode of delivery (face-to-face ; distance-learning) :
The course is given in class face-to-face. Exercises are done at home individually and independently by the students. Finally, the tutorials take place in the computer room.
Recommended or required readings :
The mandatory reference book is:
  • "Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics", C. Hirsch, 2nd ed., Butterworth-Heinemann
The electronic version can be downloaded for free through the university library.
Other recommended reading material and reference manuals include:
  • "Computational Methods for Fluid Dynamics", J.H. Ferziger & M. Peric, 3rd ed., Springer
  • "Computational Fluid Dynamics", J. Anderson, 1st ed. McGraw-Hill
  • "Fundamentals of Computational Fluid Dynamics", H. Lomax, T.H. Pulliam & D.W. Zingg, Springer
  • "An introduction to Computational Fluid Dynamics: The Finite Volume Method", H.K. Versteeg & W. Malalasekera, 2nd ed., Pearson Education Limited
  • "Fundamentals of Engineering Numerical Analysis", P. Moin, 2nd ed., Cambridge University Press
Assessment methods and criteria :
The final grade for the course is entirely based on a written exam. The exam questions are similar to the homework problem sets. The written exam is closed-book, but the students are allowed to bring a self-made handwritten 12 pages summary.
Work placement(s) :
Organizational remarks :
The course is taught in English. 
Lectures take place each Wednesday afternoon. The exact schedule and important deadlines are communicated during the first lecture.
Contacts :
Students are encouraged to actively interact with the instructor, also outside of the lectures. It is highly recommended to set up an appointment first. It is expected that the students follow a few basic rules when communicating by email: 
  • Indicate as subject "AERO0030: ...".
  • Only use ULg addresses (xxx@student.ulg.ac.be).
  • Follow the elementary rules of politeness.
Lecturer:
Prof. Vincent E. TERRAPON; MTFC Research Group; B52, 0/415; +32(0)4 366 9268; vincent.terrapon@ulg.ac.be; http://www.mtfc.ulg.ac.be/  
  Assistants:
Amandine GUISSART; B52, 0/416; +32(0)4 366 9197; amandine.guissart@ulg.ac.be
Samir SID; B52, 0/516; +32(0)4 366 4634; samir.sid@ulg.ac.be