After successful completion of the course, students are able to:

• Method of characteristics for hyperbolic scalar equations and systems.
• One-dimensional acoustics.
• One-dimensional unsteady invisicid flows, including shock

After successful completion of the course, students are able to solve the one-dimensional wave equations for acoustics, apply the method of characteristics to the solution of scalar linear advection equations, the Burgers equation, the 1D unsteady Euler equations and the 2D steady Euler equations.

The main objective of the course is to introduce the fundamentals of compressible-fluid flows, with particular reference to unsteady flows.
In particular, the theory and the relevant results for compressible-fluid flows are presented for acoustics and the unsteady one-dimensional Euler equations, with application to shock formation and propagation.

Topics: Governing equations and similarity theory. One-dimensional flows. Acoustic approximation; Wave equation; Theory of characteristics; Burgers equations; Shock waves; Rankine-Hugoniot relations; Riemann problem of gasdynamics. Method of characteristics for 2D steady problems.

The course is divided in frontal lectures (2/3 of the course) and exercise lecture (1/3 of the course). Lectures will be given in class, with the use of slides and electronic whiteboard.

Bibliography:

• Thompson, P. A., Compressible Fluid Dynamics, Editore: New York, NY: McGraw-Hill, 1972, ISBN: 9780070644052

• Anderson, J. D., Modern Compressible Flow with Historical Perspective. 2nd ed., Editore: NewYork: McGraw-Hill, 1990

The final exam is a written examination including both questions on theory and exercises.

Students are expected to have a solid knowledge on fundamentals of fluid mechanics/gas dynamics  and of aerodynamics in the incompressible regime.