322.079 Computational Aerodynamics
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2024S, VU, 3.0h, 5.0EC


  • Semester hours: 3.0
  • Credits: 5.0
  • Type: VU Lecture and Exercise
  • Format: Presence

Learning outcomes

After successful completion of the course, students are able to derive and discuss the different mathematical models used in aerodynamics (viscous/inviscid flows, compressible/incompressible flows). They will be able to recognize the character of Partial Differential Equations (parabolic, elliptic, hyperbolic) that describe these flow phenomena, and to choose and construct a suitable solution method based on proper space and time discretization. Furthermore, the students will be able to understand the basic concepts and properties of the different discretization methods (Finite Difference and/or Finite Volume methods) and to use them to compute pressure distributions and aerodynamic forces acting on an aircraft, both at low and high speeds. They will be able to understand and analyze the influence of boundary layers, shock waves, separated flow, and stall for an aircraft wing. They will be able to explain the main potentialities and drawbacks of the numerical approaches employed in the aerodynamic design of an aircraft and to describe the significance of turbulence modeling in computational aerodynamics.

The objective of the course is to learn and practice analytical and numerical tools for computing or approximating the flow around a body moving through a fluid and the forces acting on the body.

Subject of course

We will start with the potential flow theory, considering flows around basic two-dimensional bodies for which analytical solutions exist. Gradually we will introduce numerical tools that will allow us to consider bodies of general shapes. The main focus is on the flow around airplane wings. The following topics will be covered:

  • Fundamental definitions and equations of aerodynamics 
  • Euler and Navier-Stokes equations 
  • The general behavior of different classes of Partial Differential Equations (hyperbolic, parabolic, and elliptic) and their importance in understanding physical and computational aspects of aerodynamic problems at different Mach/Reynolds numbers
  • Potential Flow theory for inviscid flows 
  • Panel methods
  • Finite differences methods, approximation for first, second, and higher order derivatives
  • Truncation and round-off errors, consistency, stability, accuracy, and convergence
  • Dispersion and dissipation
  • Grid generation: Cartesian grids, stretched (compressed) grids, body-fitted structured grids, unstructured grids
  • Basics of finite volume method

Teaching methods

The range of subject matter covered in the course calls for varied teaching and learning techniques. These include lectures, tutorials, exercises/examples, and practical work. Students will be encouraged to exchange ideas and knowledge with colleagues and teachers. Several homeworks, often involving some programming skills, will be assigned throughout the semester.

A flipped classroom concept may be employed occasionally:

  • For some sessions, independent preparation will be necessary. The tasks for preparation (usually reading) will in that case be announced one week in advance in TUWEL.
  • The announced preparation is then a necessary prerequisite for participation. It will not be repeated in class.
  • It is expected that you will encounter difficulties during the preparation. Write down which difficulties you encountered, and any other questions or comments. In the class, we will discuss and clarify what you did not understand during the preparation or where you got stuck.

Mode of examination


Additional information

Programming language

  • MATLAB or simple Python (NumPy, SciPy, matplotlib)
  • Wolfram Mathematica (or Alpha) may be useful for analytical computations or Cauchy integrals.
  • Try to use a clean programming style.

Attendance is required under the standard terms:

  • Absence must be announced by email before the session.
  • Two absences are allowed.
  • Additional absences can be compensated by home assignments.
  • Online participation is possible upon request. The conditions of online participation are to be negotiated.

Communication: For questions or comments that might be of general interest to others, please use the discussion forum in the TUWEL course.

Individual consultations: 

The primary self-study material is the recommended literature listed in TUWEL. For each topic, the most relevant pages will be indicated. When multiple references are provided, you can usually select the resource which you find the most convenient. Occasionally, additional study material, slides, or summaries will be provided in TUWEL.



Course dates

Tue12:00 - 14:0005.03.2024 - 18.06.2024Seminarraum BA 08A - MB Lecture
Computational Aerodynamics - Single appointments
Tue05.03.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue12.03.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue19.03.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue09.04.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue16.04.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue23.04.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue30.04.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue07.05.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue14.05.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue28.05.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue04.06.202412:00 - 14:00Seminarraum BA 08A - MB Lecture
Tue18.06.202412:00 - 14:00Seminarraum BA 08A - MB Lecture

Examination modalities

  • Regular graded home assignments
  • Active participation in the class
  • Team project with a final technical report describing the implementation, computation, and results

Course registration

Begin End Deregistration end
14.01.2024 00:00 05.03.2024 00:00 12.03.2024 23:59

Registration modalities

Registration to the course is mandatory


Study CodeObligationSemesterPrecon.Info
066 646 Computational Science and Engineering Not specified


  • Brennen, C. E. (2016) Internet Book on Fluid Dynamics, Caltech
  • Cantwell, B. J. (2022) Fundamentals of Compressible Flow, Stanford University
  • Chattot, J.-J. (2002) Computational Aerodynamics and Fluid Dynamics, Springer
  • Fletcher, C. (1998) ‘Partial Differential Equations’ in Computational Techniques for Fluid Dynamics 1: Fundamental and General Techniques, Springer
  • Moran, J. (1984) An Introduction to Theoretical and Computational Aerodynamics, Wiley
  • Schlichting, H. and Gersten, K. (2017) Boundary-Layer Theory, 9th edition, Springer
  • Van Dyke, M. (1982) An Album of Fluid Motion, The Parabolic Press
  • Wesseling, P. (2001) ‘Classification of partial differential equations’ in Principles of Computational Fluid Dynamics, Vol. 29 of Springer Series in Computational Mathematics, Springer

Previous knowledge

  • Basic programming experience in MATLAB or Python
  • Mathematics
    • Linear algebra:
      • Operations with vectors and matrices
      • Linear and nonlinear systems of equations, Gauss elimination, Newton method
      • Eigenvalues and eigenvectors
    • Calculus: Ordinary and Partial Differential Equations
  • Interest in (fluid) mechanics, aerodynamics, and numerical methods

Continuative courses


  • Attendance Required!