Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2019/2020
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Docente Persico Giacomo Bruno Azzurro
Cfu 6.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

The purpose of the course is to present the fundamentals of computational fluid dynamics and to teach how to apply it correctly to simulate fluid machines, both of volumetric class and turbomachines. Thanks to the knowledge gained during the course, students will be able to apply CFD to design and optimize fluid machines at every operating condition. As the technical scenario includes a large variety of themes, the course is focused on the fundamentals and does not go deep into the mathematical detail of every numerical aspect.

Risultati di apprendimento attesi

At the end of the course the students will be able to translate a fluid dynamic problem, represented by PDEs, into a set of discretized equations and to solve them with appropriate numerical techniques. This will involve the knowledge of numerical stability, convergence and consistency of any discretized equation. Additionally, the students will learn about specific algorithm that are usually applied to solve compressible and incompressible flows.


Lectures and exercise sessions will allow students to:

  • Decide the most appropriate level of approximation related to the phenomena that must be simulated
  • Generate the most appropriate space discretization based on the chosen approximation level and to choose the set of boundary conditions
  • Understand the consequences of the choices made during the set-up of a CFD simulation on the result, and properly approaching the post processing phase.


The project laboratory will allow students to:

  • Generate the calculation grid
  • Set up the CFD case: boundary and initial condition
  • Monitor the simulation convergence
  • Post process the simulation results

Argomenti trattati

Basic concepts of computational fluid dynamics: Introduction to CFD. Descriptions of the main approaches used in CFD: 1D, 3D. Mathematical classification of the types of flows (compressible, incompressible, viscous, non-viscous, real or ideal gas).

Space discretization: grids for finite difference methods and for finite volume methods. Structured and unstructured grids, tetrahedral and hybrid calculation grids. Advanced meshing strategies: overset meshes.

Turbulence and its modeling: Physical meaning of turbulence. Approximation levels for the modeling of turbulent phenomena. RANS turbulence models.

Finite difference schemes: discretization of first and second derivative in space for convection/diffusion

problems. Fist order and second order methods.

Finite volume schemes: Numerical approximations of surface and volume integrals. Interpolation techniques and accuracy of the different methods. Implicit and explicit integration into time.

Solution of systems of linear equations: direct and iterative methods, elimination of Gauss, LU decomposition, method of conjugated gradients and multigrid methods.

Solution of PDE problems: definition of staggered and co-located grid SIMPLE algorithm and PISO algorithm.



Moving grid techniques: formulation of the conservation equations for control volumes with moving boundaries. Deformation of the mesh by interpolation. Movement of the calculation grid with removal and addition of cell layers. Relative movement of grids through "sliding interface" and "Generic Grid Interface" approaches. Application of mesh deformation and remapping of fields between different calculation grids.

1D methods for simulating C.I engines: State of the art. Methods for finite differences and finite volumes 1D. Method of characteristics for non-stationary flows. Resolution of the boundary conditions by method of the characteristics. Integration method of characteristics with finite difference schemes. Modeling of reacting flows.

Spray modeling: Lagrangian transport equations. Break-up models, evaporation and collision of liquid drops. Introduction to the "Finite Area" (FA) discretization. Modeling of the process of formation and evaporation of "wall film".



Flow patterns in turbomachinery: projection of equations of motion on inter-palar and meridional surfaces.


Two-dimensional flow solution around airfoils, cascades, and rotors: domain definition, grid topology, periodicity, boundary conditions for subsonic and supersonic flows. Application of turbulence models and their effects on profile losses and heat exchange. Mixing planes for multi-row configurations.


Flow solution on the meridional surface: generalized radial equilibrium. Methods based on the curvature of the flow lines. Two-dimensional throughflow methods.


Students are required to know the fundamental of fluid mechanics, fluid-machines, computational methods, and matrix algebra. Knowledge of C++ and of Linux operating system are beneficial for the students.


Modalità di valutazione

The exam will consist of a project assessment which will be carried out in groups of three-to-five students. The project is the same for all the students and is valid for a single academic year. All the groups are required to submit the report about the project by the date of the exam. The development of the project will prove that the student has learned how to discretize a system of PDEs into a set of discretized equations and how to solve them checking consistency, stability and convergence. Those students how have submitted the report within the deadline are admitted to the written examination. This will consist of two questions regarding theoretical aspects discussed during the course. This part will focus on fundamental aspects of the CFD rather than on its application. The duration of this part of the exam is 1 hour.


After the written part, all the students are required to discuss individually the project in the frame of an oral exam. Students are required to show that they can discuss the results obtained at the light of the approximations and choices they have done during the development of the project. The final mark will be a weighted average of the three parts of the exam: project, written questions and oral presentation.

Risorsa bibliografica facoltativaJ. H. Ferziger, M. Peric, Computational Methods for Fluid Dynamics, Editore: Springer, Anno edizione: 2002
Risorsa bibliografica facoltativaH. K. Versteeg, W. Malalasekera, An introduction to computational fluid dynamics: the finite volume method, Editore: Longman, Anno edizione: 1995
Risorsa bibliografica facoltativaB. Lakshminarayana, Dynamics and Heat Transfer of Turbomachinery, Editore: John Wiley & Sons, Anno edizione: 1996

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 60:00 90:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
schedaincarico v. 1.6.1 / 1.6.1
Area Servizi ICT