Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Academic calendar
The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technicaladministrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.
Course calendar
The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..
Period  From  To 

I semestre  Oct 1, 2019  Jan 31, 2020 
II semestre  Mar 2, 2020  Jun 12, 2020 
Session  From  To 

Sessione invernale d'esame  Feb 3, 2020  Feb 28, 2020 
Sessione estiva d'esame  Jun 15, 2020  Jul 31, 2020 
Sessione autunnale d'esame  Sep 1, 2020  Sep 30, 2020 
Session  From  To 

Sessione estiva di laurea  Jul 22, 2020  Jul 22, 2020 
Sessione autunnale di laurea  Oct 14, 2020  Oct 14, 2020 
Sessione autunnale di laurea solo triennale  Dec 10, 2020  Dec 10, 2020 
Sessione invernale di laurea  Mar 16, 2021  Mar 16, 2021 
Period  From  To 

Festa di Ognissanti  Nov 1, 2019  Nov 1, 2019 
Festa dell'Immacolata  Dec 8, 2019  Dec 8, 2019 
Vacanze di Natale  Dec 23, 2019  Jan 6, 2020 
Vacanze di Pasqua  Apr 10, 2020  Apr 14, 2020 
Festa della Liberazione  Apr 25, 2020  Apr 25, 2020 
Festa del lavoro  May 1, 2020  May 1, 2020 
Festa del Santo Patrono  May 21, 2020  May 21, 2020 
Festa della Repubblica  Jun 2, 2020  Jun 2, 2020 
Vacanze estive  Aug 10, 2020  Aug 23, 2020 
Exam calendar
Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.
Academic staff
Mazzuoccolo Giuseppe
giuseppe.mazzuoccolo@univr.it +39 0458027838Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University. Please select your Study Plan based on your enrolment year.
Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

1° Year
Modules  Credits  TAF  SSD 

2° Year activated in the A.Y. 2020/2021
Modules  Credits  TAF  SSD 

3° Year activated in the A.Y. 2021/2022
Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

Legend  Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Fluid dynamics (2021/2022)
Teaching code
4S00258
Teacher
Coordinatore
Credits
6
Language
Italian
Scientific Disciplinary Sector (SSD)
INGIND/06  FLUID DYNAMICS
Period
Secondo semestre dal Mar 7, 2022 al Jun 10, 2022.
Learning outcomes
Derivation of the fluiddynamic equations from conservation laws in Physics; discussion on the rheological structure of fluids and the model for Newtonian fluids; different flows and simplifications of the governing equations; Bernoulli theorem in all forms and for all cases; some exact solutions; vorticity dynamics; laminar boundary layer; stability and transition; turbulence; hyperbolic equations in fluid dynamics. Numerical resolution in Matlab / Octave of some typical problems of fluid dynamics.
Program
The teaching prerequisites are: differential and integral calculus in one and two variables, numerical methods for the solution of equations and systems of nonlinear equations, basic numerical methods for differential equations, such as explicit Euler and the finite difference method.
1. Introduction to fluids: definitions, continuous hypothesis and properties of fluids; differences between fluid, flux, flow; some kinematics (streamlines, trajectories, streaklines), forces and stresses (Cauchy Theorem and symmetry of the stress tensor), the constitutive relation for Newtonian fluids (viscous stress tensor).
2. Governing equations: Eulerian vs Lagrangian approach; control volume and material volume, conservation of mass in a fixed volume, time derivative of the integral over a variable domain, Reynolds Theorem (scalar and vectorial forms), conservation of mass in a material volume, from conservation laws to the NavierStokes equations, the complete NavierStokes equations (in conservative, tensorial form), substantial derivative, conservative vs convective form of the equations, alternative forms of the energy equation, dimensionless equations, initial and boundary conditions.
3. Particular cases of the governing equations: time dependence, effect of viscosity, thermal conduction, entropy, compressibility, barotropic flows, incompressible flows, ideal flows, Euler equations irrotational flows, barotropic and nonviscous flows: Crocco's form, Bernoulli theorem in all cases and forms.
4. Some exact solutions: incompressible and parallel flows, infinite channel flow, Couette and Poiseuille flows, flow in a circular pipe, HagenPoiseuille solution.
5. Vorticity dynamics: preliminary definitions, vorticity equation in the general case, special cases (constant density, nonviscous flow with conservative external field), Kelvin's theorem, Helmholtz's theorems and their geometrical meaning.
6. Laminar boundary layer: Prandtl theory, boundary layer past a flat plate, derivation of Blasius' equation (similar solutions), boundarylayer thickness, drag due to skinfriction, characteristics of a boundary layer (displacement thickness, momentum thickness, shape factor), integral von Kàrmàn equation, numerical solution of the 2D steady equations for the boundary layer past a flat plate:
(a) parabolic PDE + BC (Prandtl's equations): marching in space
(b) ODE + BC (Blasius' equation): nonlinear boundary value problem
(c) comparison between the two methods.
7. Stability and transition: flow in a pipe  Reynolds' experiment, transition in a laminar boundary layer, linear stability for parallel flows (OrrSommerfeld equation),
Squire's theorem, nonviscous stability (Rayleigh's criteria), viscous stability, linear stability curves.
8. Turbulence: phenomenological characteristics, turbulent scales, energy cascade, Kolmogorov's theory, DNS (Direct numerical simulation), RANS (ReynoldsAveragedNavierStokes equations), the problem of closure for the RANS, closure models, Boussinesq hypothesis for the tutbulent viscosity (models of order 0, 1 and 2), LES (Large Eddy Simulation).
9. Hyperbolic differential equations in fluid dynamics: main characteristics and comparison with parabolic and elliptic equations, conservation laws, transport equation, characteristic lines, Riemann problem, Burgers' equation, weak solutions, shock waves, rarefaction waves, comparison between conservative and nonconservative numerical methods, method of characteristics, usage of an applet for the visualization of shock and rarefaction waves, hyperbolic linear and nonlinear systems, genuine nonlinearity, linear degeneration, contact discontinuity, solution of the Riemann for the Euler equations.
Examination Methods
The aim of the exam is to ensure that the student is able to produce and recognize rigorous demonstrations, mathematically formalize natural language problems and discuss mathematical models for fluid dynamics analyzing their limits and applicability. The exam consists of an oral interview on the course program and the discussion on the numerical exercises in Matlab/Octave assigned during the course. The discussion on the latter aims to ensure that the student is able to use computer tools, programming languages, and specific software.
Type D and Type F activities
years  Modules  TAF  Teacher 

1° 2° 3°  Python programming language  D 
Maurizio Boscaini
(Coordinatore)

1° 2° 3°  SageMath  F 
Zsuzsanna Liptak
(Coordinatore)

1° 2° 3°  History of Modern Physics 2  D 
Francesca Monti
(Coordinatore)

1° 2° 3°  History and Didactics of Geology  D 
Guido Gonzato
(Coordinatore)

years  Modules  TAF  Teacher 

1° 2° 3°  C Programming Language  D 
Sara Migliorini
(Coordinatore)

1° 2° 3°  C++ Programming Language  D 
Federico Busato
(Coordinatore)

1° 2° 3°  LaTeX Language  D 
Enrico Gregorio
(Coordinatore)

years  Modules  TAF  Teacher 

1° 2° 3°  Corso Europrogettazione  D  Not yet assigned 
1° 2° 3°  Corso online ARPM bootcamp  F  Not yet assigned 
1° 2° 3°  ECMI modelling week  F  Not yet assigned 
1° 2° 3°  ESA Summer of code in space (SOCIS)  F  Not yet assigned 
1° 2° 3°  Google summer of code (GSOC)  F  Not yet assigned 
Career prospects
Module/Programme news
News for students
There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and soon also via the Univr app.
Graduation
Attachments
Title  Info File 

1. Come scrivere una tesi  31 KB, 29/07/21 
2. How to write a thesis  31 KB, 29/07/21 
5. Regolamento tesi (valido da luglio 2022)  171 KB, 17/02/22 
List of theses and work experience proposals
theses proposals  Research area 

Formule di rappresentazione per gradienti generalizzati  Mathematics  Analysis 
Formule di rappresentazione per gradienti generalizzati  Mathematics  Mathematics 
Proposte Tesi A. Gnoatto  Various topics 
Mathematics Bachelor and Master thesis titles  Various topics 
THESIS_1: Sensors and Actuators for Applications in MicroRobotics and Robotic Surgery  Various topics 
THESIS_2: Force Feedback and Haptics in the Da Vinci Robot: study, analysis, and future perspectives  Various topics 
THESIS_3: CableDriven Systems in the Da Vinci Robotic Tools: study, analysis and optimization  Various topics 
Stage  Research area 

Internship proposals for students in mathematics  Various topics 
Attendance
As stated in the Teaching Regulations for the A.Y. 2022/2023, except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended onsite.
Please refer to the Crisis Unit's latest updates for the mode of teaching.