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CODE 60369
SEMESTER 2° Semester


The course aims at providing the students with modern instruments to enable shape optimization in fluid dynamics. In the first part of the course different methods are presented, such as Deterministic optimization, Design of Experiment, Response Surface Modelling, Stochastic Optimization and Robust Design Optimization. In the second part the students will learn some industrial open source codes (Dakota and OpenFOAM) and perform shape optimization of realistic cases. The final exam is a project. 



The objective of the course is to provide students with useful and modern tools to make shape optimization in the field of fluid dynamics. In the first part of the course the theory of the various optimization methods is presented, including deterministic optimization, Design of Experiment (DoE), surface response (RSM), stochastic optimization and robust design. In the second part of the course, practical examples, such as optimization of a wing profile and a convergent / divergent conducts, are analyzed with open source industrial tools (Dakota and OpenFOAM).


Attendance and active participation in the proposed training activities (lectures, exercises and numerical exercises) and individual study will allow the student to:

  • know the fundamentals of numerical optimization;
  • understand the differences between deterministic, stochastic and robust optimization;
  • provide examples of application of optimization in the field of fluid dynamics to current life and process engineering; estimate calculation times and method to be used;
  • determine optimal and sub-optimal solutions;
  • critically discuss the approximations introduced and the results obtained.
  • apply industrial codes such as openfoam and Dakota


Basic knowledge of aerodynamics, transition and turbulence is required for successful learning


The lessons are divided into theory and practice. All the theory presented in the course is used in the exercises so that students can apply what they have learned and understand the difficulties in the applications. The exercises are both written and computer programming. Students are requested to bring their own computer and to install Matlab for which a student license is available.

Working students and students with DSA, disability or other special educational needs certification are advised to contact the teacher at the beginning of the course to agree on teaching and exam methods which, in compliance with the teaching objectives, take into account individual ways of learning.


Ikon för Verifierad av gruppen



The program of the module includes the presentation and discussion of the following topics:

Deterministic optimization
The sensitivity part concerns, in general, the study of the variation of the response/output of a function with respect to the variation of the input of the same function. For instance; how much the drag of a wing changes due to a small change in the angle of attack. In other words, how sensitive is the resistance to a small change in angle of attack. Often the function in question is not an explicit function of the input. Resistance is a function of velocity and pressure which are often the solution of ODE or PDE equations. Sensitivity is a quantity of interest in itself but is often used in the context of deterministic (gradient-based) optimization.
The most effective way of assessing sensitivity is by using the adjoint equation; a linear equation that derives from the direct/physical equation of the problem. The derivation of sensitivity for stationary and unsteady problems is treated in the course together with the definition of the adjunct and its derivation in different applications.
Constrained optimization using Lagrange multipliers is also taught in this part. It is shown how the multipliers coincide with the solution of the adjoint equation of the physical problem. Furthermore, we study how to solve nonmodal stability problems by calculating the optimal perturbation; the initial condition that gives life to the greatest growth of the system for a given finite time.

Nonmodal stability
The study of stability concerns the response/evolution of small perturbations in space or time (spatial or temporal stability). The stability of a system is often studied to predict bifurcations or the transition of a system; for example the transition from laminar to turbulent flow or the unsteady wake
back a cylinder or a car. Nonmodal stability concerns the evolution of perturbations considering a finite time or space. In other words, the initial transitional period. In this part we study the various ways of calculating nonmodal growth through superposition of normal modes, Singular Value Decomposition, optimization and analytical solutions.

Design of Experiment (DoE)
In this part we study the techniques of; randomized complete block design, latin square, full factorial, fractional factorial, central composite, Taguchi, random, Sobol, latin hypercube.

Response Surface Modeling (RSM)
In this part we study the techniques of; least squares, Shepard, K-nearest, Kriging, Radial Basis Functions, AAN​

Stochastic Optimization
In this part we study the techniques of; multi-objective optimization, Pareto front when there are no dominant solutions, simulated annealing (SA), particle swarm optimization (PSO), game theory optimization (GT), evolutionary algorithms (EA), genetic algorithms (GA)

Introduction to Ansys Fluent, Onshape
As preparation for the development of projects we propose a brief introduction of the Onshape software, as a CAD tool, and Ansys Fluent as a CFD solver and optimization.

At the beginning of the course the students will choose, together with the teacher, a project taken from the course content that will be treated both theoretically and numerically. These "mini" projects will be summarized in an article/report that will be presented at the end of the course. A sample article / report on the style to be used will be made available and discussed at the beginning of the course.

In the course the Matlab software is used for programming tasks in the classroom. In the second part of the course, and for the project, Ansys Workbench software is used. All software is available under license for Unige students.


Notes and other material will be provided by the instructor and the following textbooks are suggested:

Nocedal, J. & Wright, S.J.,1999, "Numerical optimization", Springer

Henningson, D.S. & Schmid, P.J., 2001, "Stability and transition in shear flows", Springer

LeVeque, R.J.,1998, "Finite Difference Methods for Differential Equations", University of Washington



Class schedule

The timetable for this course is available here: Portale EasyAcademy



The course program includes a written exam during the lecture period and the presentation, including a written report, of a project at the end of the course. The final grade is mainly based both on the project and partly on the exam.


Details on how to prepare for the exam and the degree of depth of each topic will be given during the lessons.
The written exam will verify the actual acquisition of basic knowledge on some methodologies and their applications for analysis.
The project can be carried out after the end of the course and the presentation agreed with the teacher before the end of the academic year. It will be evaluated

  • the content of the project (planning, analysis, care in the development, choice of methods and results obtained)
  • the report (correctness in the setting; abstract, introduction, method, results, discussion, bibliographical references)
  • the presentation (content, logic, aesthetics, clarity)


Ikon för Verifierad av gruppen




Students with SLD, disability or other special educational needs certification are advised to contact the teacher at the beginning of the course to agree on teaching and exam methods that, in compliance with the teaching objectives, take into account the modalities learning opportunities and provide suitable compensatory tools.

Agenda 2030 - Sustainable Development Goals

Agenda 2030 - Sustainable Development Goals
Affordable and clean energy
Affordable and clean energy
Responbile consumption and production
Responbile consumption and production