Agenda 2023

The talk presents the theory of transition and turbulence. During these lesson , the participants will be exposed to the basic concepts of hydrodynamic stability and turbulence, and a short introduction on high-fidelity numerical methods (spectral methods). : i) stability, classical (waves) and non-modal (streaks) ii) iii) wall-bounded turbulence, scaling laws, resolution iv) coherent structures and simple way of extraction (POD) The second part will focus into the numerical modeling by spectral methods: i) introduction to spectral methods ii) Accuracy and UQ iii) Fourier-Chebyshev method for channel flow, incl. pressure correction

Hands-on session with Nek5000 hands-on 5: Nek5000 in 2D (eddy_uv and cavity) – hands-on 6: airfoil at low Re

brief introduction to the speakers and bio

The modelling and the computational issues involved in the accurate simulation of turbulent multiphase flows will be presented. The available numerical models/ methods currently used will be described, with a specific focus on the phase field method, which will be discussed in connection with interface resolved simulations of bubbles- and droplets-laden turbulent flows.

The most recent high-performance computing architectures, parallelization techniques, and scientific visualization tools will be presented in connection with the use of computational methods of interface resolving simulations of turbulent flows. During the hands-on sessions, students will have the opportunity to test the different methodologies and tools.

This course is meant to introduce attendants to the basic principles of numerical discretization of the compressible Navier-Stokes equations. Introductory concepts related to the mathematical properties will be provided, with special emphasys on the identification of integral invariants Analysis of numerical methods based on linear and nonlinear Fourier analysis will be presented. Principles of energy-consistent discretizations of the convective terms will be outlined, both for model equations and for the full Navier-Stokes equations.

This part of the course will be devoted to the analysis of shock-capturing schemes. Basic discretization techniques including the TVD, ENO, and WENO methods will be introduced. Tools for weakly nonlinear analysis of baseline schemes will be introduced. Efficient hybrid implementation strategies based on use of shock sensors will be outlined.

The lecture will familiarize the students with STREAmS, an open-source flow solver developed to perform large-scale simulations of canonical wall-bounded flows for fundamental understanding of turbulence in the high-speed regime.

The hands-on tutorials planned in the second part of the lecture will provide the students with the possibility of performing numerical simulations with STREAmS using graphical processing units (GPUs), which grant accelerated cutting-edge performance with high energy efficiency.

The history and the basic principles of the Immersed-boundary method will be introduced, including baseline grid tagging procedures, forcing methods and boundary reconstruction. Proper treatment of problems including moving bodies will be illustrated, as well as use of turbulence models. Examples of numerical applications will be presented.

This course aims to introduce attendants fo the basic principles of numerical simulations in complex domains using the chimera approach. The following topics will be dealt with: curvilinear mesh generation; overlapping grids and interpolation procedures. Implementation of high-order schemes and extension to compressible flows will be discussed. Numerical examples will be provided.

The goal of this tutorial is to introduce participants to use of the immersed-boundary method within the framework of the AFID incompressible flow solver. Proper set-up of selected flow problems will be illustrated, as well as data processing and visualization.