Numerical simulation in fluid mechanics (or CFD) has become one of the basic tools used by engineers. In this course, we will study the methods often used in industrial codes and we will give the most active research strategies which will be the future standards. This course does not aim at teaching the practical use of a CFD code, rather at providing the key knowledge to understand what the codes contain and how to use them in a wise manner. Prerequisites: For this course, it is necessary to have attended a course of introduction to turbulence The main tackled points are: 1. Introduction to CFD (Computational Fluid Dynamics) ◦ Different phases and important points of a simulation: geometric modelling, meshing, physical modelling, computation, post-processing, ◦ Evaluation of computational costs linked with turbulence, computer power available today and conclusions for modelling, ◦ Different existing methods (RANS, hybrid, LES, DNS) : objectives, formalism, modelling, maturity, fields of application, ◦ Global picture of CFD codes: commercial codes (Fluent, StarCD, CFX, Powerflow…), « in-house » industrial codes, open-source codes (Open-Foam, Code_Saturne). 2. Standard method used in industrial projects: RANS modelling (Reynolds-averaged Navier-Stokes modelling): ◦ Closure problem, different levels of modelling, history, ◦ Similarity with continuum mechanics (constitutive relations), physical principles, ◦ Eddy-viscosity modelling: hypotheses, selection of the constitutive relation, k-epsilon models, k-omega models, Spalart-Almaras model, etc.: limits, corrections, variations, ◦ Reynolds-stress modelling: hypotheses, advantages, limits, algebraic modelling, ◦ Wall regions: physics, joint selection of the mesh and the model, law of the wall, low-Reynolds number models, 3. More expensive methods: ◦ Large-eddy simulation (LES): filtering, subgrid-scale stresses, modelling, fields of application, ◦ Hybrid RANS/LES methods: • zonal methods: principle, interface modelling, • continuous methods: formalism, URANS, OES, VLES, SNS, DES, SBES, SAS, PANS, PITM, HTLES