The goal of the course is to provide the students with an "advanced user / beginner developer" level in computational fluid dynamics, with a focus on compressible flows of interest in aerospace and energy applications. Following the course, the student should be able to properly select and apply a solution method for an engineering problem of practical interest and should understand the observed numerical behaviour (accuracy, robustness). The student will also be able to perform basic developments in existing CFD codes: change of boundary conditions or implementation of a new numerical flux.
Lecture #1: Introduction to CFD. From pioneering works to 21st century challenges.
Lectures #2 and #3: Analysis of scalar problems : classification of PDEs, method of characteristics, finite difference schemes for model problems : 1D advection, 1D diffusion, 1D advection-diffusion.
Lectures #4 and #5: Extension of 1D finite-difference schemes to non-linear systems of conservation laws (Euler equations): from the 1st-order upwind scheme to high-resolution schemes.
Lectures #6 and #7: Finite-Volume Schemes in structured and unstructured grids. From Euler equations in Cartesian grids to the Navier-Stokes equations in triangular grids.
Lecture #8 : Introduction to spectral methods.