Introduction to Computational Fluid Dynamics

In this introductory course we shall discuss simple methods to solve a simple nonlinear problem for the Navier-Stokes equations of Fluid Dynamics. To give support to our calculations, we will treat in detail many topics such as finite-differences, time integration, stability, and numerical linear algebra.

• Time integration (stability, forward, backward and midpoint Euler, Crank-Nicolson, leapfrog, Runge-Kutta, multistep methods.)

• Finite differences

• Numerical linear algebra (Gaussian elimination, LU and QR decomposition, conjugate gradients, eigenproblems)

• Poisson problem (Gauss-Seidel iteration, successive over-relaxation,multigrid,fast Fourier transform)

• Hyperbolic equations (Lax-Friedricks,Crank-Nicolson,Lax-Wendroff,MPDATA)

• Special topics depending on the specific interests of the students attending the course (particle-based methods, Lattice Boltzmann, spectral methods,vortex methods).

1. Hinch EJ. Think Before You Compute: A Prelude to Computational Fluid Dynamics. Cambridge University Press; 2020.

2. Lautrup B., Physics of Continuous Matter: Exotic and Everyday Phenomena in the Macroscopic World. Taylor & Francis; 2011.

3. Carnahan B., Luther, H.A. and Wilkes, J.O. Applied Numerical Methods. Wiley; 1969.

The completion of this course will be assessed based on:

- 60% theoretical and numerical home exercises,

- 40% written report on the main numerical project performed by the student.

Attendance at lectures and tutorials is encouraged, but is not compulsory.