B027567 - MATHEMATICAL MODELS OF FLUID DYNAMICS

ITALIAN

Incompressible gasdynamics
Compressible gasdynamics
Newtonian fluids
Turbulence (hints).

1) Moodle learning platform: Lectures Note.

2) A.J. Chorin, J. E. Marsden: A mathematical introduction to fluid mechancs, Springer, 1980.

3) C. Trusdell, K.R. Rajagopal: An introduction to fluid mechanics, Birkhauser, 2000.

The course aims to provide the students with fundamental knowledge and understanding about mathematical modeling in fluid mechanics. One of the aims is to let the students develop basic technical skills, and critical thinking, needed when modeling and solving mathematical problems in different settings. Special attention will be paid to help the students to develop communication skills necessary for teamwork. The course covers topics and provides learning skills that are important in applied mathematics and scientific calculus.

Lectures: Presentation of the theory described in the course program, with teacher-student direct interaction, to ensure a full understanding of the subject.

Office hours Prof. Farina, by prior appointmentDipartimento di Matematica e Informatica "Ulisse Dini"
Viale Morgagni, 67/a
50134 - Firenze (FI)
Tel: 055 2751435
E-Mail: angiolo.farina@ unifi.it

Final oral examination. A number of questions are posed. The oral examination is designed to evaluate the degree of understanding of the theory presented in the course. In the assessment, special attention is paid to communication skills, critical thinking and appropriate use of mathematical language.

INCOMPRESSIBLE GASDYNAMICS
• Ideal and incompressible fluids and their dynamics• Vorticity• Bernulli theorems, Lagrange-Thompson• Contour conditions• Stream function and potential function• External flow and aerodynamic action• D'Alambert's Paradox• Kutta-Joukowski's theorem• Conformal transformations• Plate, circle arch and generic Jukoswski profile.

COMPRESSIBLE GASDYNAMICS
• Thermodynamics of perfect fluids.• Sound speed, Mach number, fluid compressibility.• Sound waves.• Supersonic flows around thin profiles.• Characteristics lines.• Riemann Invariants• Prandtl-Meyer flows• Shock waves• Wave flat discontinuity finished. Rankine-Hugoniot Relations.• Uniqueness and condition of entropy.

NEWTONIAN FLUIDS
• Dynamics of incompressible Newtonian fluids• Equations by Navier-Stokes• Vorticity in Newtonian Fluids• Reynolds Number, laminar and turbulent regime• Some laminar flows: Hagen-Poiseuille and Couette• Laminar boundary layer• Exact solutions for flat plate• Laminar separation

TURBOLENCE (hints)