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.

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

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.

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: 

• Wednesdays, 14:00 - 16:00
• Getreidemarkt 9, BA, 7th floor, BA07G08. Dial 32214 with the phone on the wall.

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.

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

Registration to the course is mandatory

• 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

• 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