Optimization in Fluid Mechanics

(Optimierung in der Strömungsmechanik)

Lecturer: Prof. Nicolas R. Gauger, Beckett Zhou, Tim Albring
Date and Place:
Lecture: Wednesdays, 08:15h – 09:45h, SC Seminar Room 32-349
Exercises: Tuesdays, 08:30h – 10:00h, Room 34-420 (bi-weekly)
Note: First introductory lecture will be on 19.04., 08:15h – 09:45h.
ECTS: 4.5
Language: German or English


Master students in mathematics and computer science. Preferably with some basic knowledge about PDEs and numerics.


We will introduce and investigate several methods (for example adjoint and one-shot methods) for the efficient numerical solution of shape optimization problems in fluid mechanics and questions in optimal active flow control.
In the exercise the acquired methods for optimization in fluid mechanics will be implemented within the open-source fluid solver SU2 (http://su2.stanford.edu) and applied to practical optimization problems.



  • Governing equations for fluid mechanics
  • Reynolds-averging and turbulence modeling
  • Finite volume method
  • Objective functions and constraints
  • Shape optimization in fluid mechanics
  • Optimal active flow control
  • Continuous and discrete adjoint methods
  • One-shot methods


  • LeVeque, R.: Numerical Methods for Conservation Laws, Lectures in Mathematics. ETH Zürich
  • Hirsch, C.: Numerical Computation of Internal and External Flows, Vol. 1 & 2, Wiley
  • Blazek, J.: Computational Fluid Dynamics: Principles and Applications, Elsevier
  • Mohammadi, B.; Pironneau, O.: Applied Shape Optimization for Fluids, Oxford University Press
  • Griewank, A.; Walther, A.: Evaluating Derivatives, Principles and Techniques of Algorithmic Differentiation, Second Edition, SIAM
  • Naumann, U.: The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation, SIAM

Lecture material will be available in the OLAT website of the course:

KIS Link