This course focuses on numerical methods for solving multiscale partial differential equations,
with applications to compressible fluid dynamics across different Mach number regimes.
Implicit and explicit approaches are introduced through the advection-diffusion equation,
followed by an analysis of the Euler equations for compressible gas dynamics in non-dimensional
form and their asymptotic limits. The concept of Asymptotic Preserving (AP) schemes is explored
through IMEX and semi-implicit formulations. A significant part of the course is devoted to
a hands-on Matlab implementation of a semi-implicit scheme for the one-dimensional Euler
equations. The course concludes with an outlook on advanced topics, including high-order IMEX
methods and exactly divergence-free operators.
Timetable:
Wednesday 10/12/2025: room ALFA (9:30-12:30)
Thursday 11/12/2025: room H (9:00 - 12:00)
