D1 - Knowledge and understanding
At the end of the course, the student will have to know the basic aspects of the subject and the principles of computational fluid dynamics
D2 - Ability to apply knowledge and understanding
The student must be able to perform numerical simulations of computational fluid dynamics and to give the correct physical interpretation to the numerical results
D3 - Making judgments
At the end of the course, the student must be able to carry out a critical examination to verify the correct application of the knowledge acquired and applied to the physical-mathematical problem studied
D4 - Communication skills
At the end of the course, the student must be able to correctly illustrate the acquired knowledge and practical skills with the correct use of technical terms
D5 - Learning ability
The student must be able to deal with the study of basic fluid dynamics problems to support advanced fluid dynamics courses

Mathematical physics knowledge necessary for the study of continuum
mechanics, including tensor analysis

Part I:
Introduction to fluid dynamics, fluid properties, fluid statics, kinematics, conservation laws
conservation of mass, momentum
and energy, vorticity, dimensional analysis, boundary layer, analytical solutions
Part II
Principles of numerical methods, numerical solution of the advection-diffusion equation, laminar solutions with the software Openfoam

Fluid Mechanics, authors: P. K. Kundu, I. M. Cohen; D. R. Dowling,
Academic Press
Computational Techniques for Fluid Dynamics 1, di C.A.J. Fletcher

Part I: fundamentals

1) Introduction to fluid dynamics
a. fluid properties
b. the laws of thermodynamics
c. Molecular transport phenomena

2) Kinematics
a. Eulerian and Lagrangian approach
b. flow lines, acceleration of a fluid element
c. Relative motion between two points: The deformation rate and rotation tensors
d. Reynolds Transport Theorem
3) Hydrostatics
a. isotropy of pressure
b. differential equation of statics
c.hydrostatic distribution of pressure
d. measure of pressure
e. Immersed bodies
f. rigid motion of a fluid
4) Conservation laws
a. conservation of mass
b. Conservation of momentum
c. constitutive laws
d. Navier-Stokes equations
e. non-inertial reference systems: The Coriolis force
f. Bernoulli's Principle

5) Dynamics of vorticity
a. Kelvin theorem
b. of Helmholtz theorem
c. Vorticity equation in inertial reference system
d. Interaction between irrotational vortexes
6) Dimensional analysis
a. non-dimensional forms of conservation laws
b. Theorem  Buckingham
c. The laboratory tests
8) The boundary layer theory
a. definitions
b. analytical solution for flat plate
c. boundary layer separation
d. Notes to flow around bluff bodies
e. Lift and drag
7) Laminar flows
a. analytical solutions of parallel flows
b. self-similar solutions

Part II: computational fluid dynamics

1) finite difference method, finite volume method
2) how to solve a differential equation with finite difference method (writing a code, languages used by the student: matlab, fortran, c ++, python ..)
3) implicit and explicit methods, applied for example for the solution of the diffusion equation
4) concepts of stability, consistency and convergence of a numerical scheme
5) classification of PDEs, boundary conditions, and examples of possible numerical schemes that can be used to solve these equations (including iterative methods for stationary equations)

6) use of OpenFOAM software: how to build a grid and how to set up the simplest cases (2D Poiseuille flow and lid-driven cavity)
7) look inside OpenFOAM, the various solvers and numerical schemes that can be used and other details of how the software works (finite volume method)
8) build complex calculation grids, with OpenFOAM. For example, flow around an immersed body.

frontal lessons,
exercises and laboratory activities

Oral presentation of the arguments developed during the course and the
solution of exercises.
Written report concerning a numerical solution of the transport-diffusion
equation and two test cases reproduced with OpenFOAM: lid driven cavity
and Poiseuille flow.