Numerical methods in fluid dynamics

This short course is part of the international master program Factory of the future proposed by Arts et Métiers Institute of Technology. This course is not mandatory. Hence, having only a handful of students enrolling each year, it consists in a series of hands-on tutorials rather than dedicated lectures. The aim is that, by the end of the course, students are able to implement in python a simple two-dimensional Navier-Stokes solver based on pseudospectral methods for two-dimensional turbulence in a doubly periodic domain.

Prerequisite

• Basic mathematics (e.g. derivative and integrals, complex numbers, Fourier analysis).
• Prior knowledge of python, octave or matlab would be beneficial.

Lesson plan

This course consists in a series of tutorials.

• Tutorial 1: Solving the stationary heat equation.
• Tutorial 2: Solving the one-dimensional linear advection-diffusion equation in a periodic domain.
• Tutorial 3: Solving the one-dimensional Burger’s equation in a periodic domain.
• Tutorial 4: Towards a Navier-Stokes solver for two-dimensional turbulence in a doubly periodic domain.

Recommended reading

• TBA

Additional resources

• SciPy lectures
• 12 steps to Navier-Stokes by L. Barba.