2023-2024 / AERO0030-1

Computational fluid dynamics


30h Th, 20h Pr, 10h Labo.

Nombre de crédits

 Master : ingénieur civil en aérospatiale, à finalité5 crédits 
 Master : ingénieur civil physicien, à finalité5 crédits 


Vincent Terrapon

Langue(s) de l'unité d'enseignement

Langue anglaise

Organisation et évaluation

Enseignement au deuxième quadrimestre


Horaire en ligne

Unités d'enseignement prérequises et corequises

Les unités prérequises ou corequises sont présentées au sein de chaque programme

Contenus de l'unité d'enseignement

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)

Acquis d'apprentissage (objectifs d'apprentissage) de l'unité d'enseignement

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
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, III.1, III.2, III.3, IV.1, IV.3, VI.1 of the MSc in aerospace engineering.

This course contributes to the learning outcomes I.1, I.2, II.1, II.2, III.1, III.2, III.2, III.3, III.3, IV.1, VI.1 of the MSc in engineering physics.

Savoirs et compétences prérequis

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.

Activités d'apprentissage prévues et méthodes d'enseignement

The formal lectures take place each week for about 2-3 hours. They focus on the theoretical concepts that are illustrated by numerous examples. Additionally, students should regularly read the accompanying textbook to consolidate their understanding of this theory.

Homework problems are also distributed every week. Students are expected to work on them on their own. These problem sets consist in solving analytical exercises or developing small programs in Matlab. They illustrate the concepts seen in class and help further 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, or to post them on the forum. 

Additionally, five tutorials are organized after the formal lectures. Their objective is to illustrate the theoretical concepts seen in class through real case examples. These tutorials are based on concrete simulation examples relying on the OpenFOAM and/or SU2 solvers. A virtual box containing the required tools and examples is provided. The five tutorial sessions take place in the CAD computer room or in the classroom depending on the number of students. In the latter case, the students will need to have their laptop with the virtual box installed.

Mode d'enseignement (présentiel, à distance, hybride)

Cours donné exclusivement en présentiel

Explications complémentaires:

The course is given in class face-to-face. Podcasts of the lectures are available on the course webpage.

Exercises are done at home individually and independently by the students.

The tutorials take place in the computer room or in the classroom depending on the number of students. In the latter case, the students should take their laptop and install the virtual box.

Lectures recommandées ou obligatoires et notes de cours

The course material (lecture slides, problem sets, podcasts, ...) are posted each week on the course website: www.mtfc.uliege.be/CFD.

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. L'utilisation du VPN ou du réseau de l'université est nécessaire pour accéder le fichier pdf.

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

Modalités d'évaluation et critères

Examen(s) en session

Toutes sessions confondues

- En présentiel

évaluation écrite ( questions ouvertes )

Explications complémentaires:

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 one-sided page summary.


Remarques organisationnelles et modifications principales apportées au cours

The course is taught in English. 

Lectures take place on Tuesdays. The exact schedule and important deadlines are communicated during the first lecture.

Depending on the sanitary situation, changes in the organization might be necessary. 

There is no major change with respect to previous year.


Students are encouraged to actively interact with the instructor, also outside of the lectures. It is 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.uliege.be).
  • Follow the elementary rules of politeness. 


Prof. Vincent E. TERRAPON; MTFC Research Group; B52, 0/415; +32(0)4 366 9268; vincent.terrapon@uliege.be; http://www.mtfc.uliege.be

Association d'un ou plusieurs MOOCs