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Mathematical problems laying beneath solving dynamic real-world problems, such as modelling water flows around turbines, wind turbulence around the aerodynamic design of a vehicle or boat, improving turbine engine performance, modelling of weather predictions, etc. are quite large in size due to many variables involved and the complex physics. On top of that, they present time dependency problems, meaning the obtained solutions change (have to be recalculated) through time steps -at every second or even at smaller steps. Solving such problems is not a simple task and the use of HPC technologies and infrastructures enables more accurate analysis. The participants will be introduced with different approaches and also broaden their perspective. To achieve this objective, they will have to embrace both programming skills as well as advanced numerical simulation skills.


The distribution of covered topics through 5 days of training. Each day is dedicated to a specific numerical method/class of problems. The students will be follow-through from the basicnumerical method, up to their implementation in HPC, and massively parallel applications.
  • Day 1; Morning: training orientated on introducing to HPC as a tool and related super-computing tools. The state of the art of HPC infrastructures will be presented; a re-cap will be given on the principles of parallel computing paradigms on standard and heterogeneous architectures. For the purpose of training event management usage of the e-learning platform has to be explained. Each participant will participate with computer and will be granted access to a local HPC.Afternoon: Numerical methods for unstructured finite-volume general-purpose solvers based on the OpenFOAM framework. Example taken from full-scale engineering applications will be shown bytop-class experts from academia, industries of Release Authorities.
  • Day 2; Morning: Numerical Methods for compressible/high-speed flow with finite differences schemes plus shock-capturing (ENO/WENO)Afternoon: High-order methods: Numerical Methods for compressible/high-speed flow: Discontinuous Galerkin methods (theory and hands-on), with a focus on the EU project Hi-Fi TUrb
  • Day 3; Morning: Physics and high-performance computation of turbulent flows with interfaces. Simulations of interfaces in TurbulentFlows with Breakage, Coalescence and Drop Size Distribution -Phase Field & DNS (theory and hands-on)Afternoon: Preconditioning techniques for large linear systems, theory and industrial applications
  • Day 4; Numerical modelling with Immersed boundary techniques: theory and hands-on (AFiD code)Optional: training and presentation on commercially available software widely used by communities / SMEs.
  • Day 5; Morning: Spectral methods and spectral element methods with a focus on Nek5000 (link to past EU project Excellent)Afternoon: Presentation of a high demanding research or innovation project and solution with the usage of HPC. This is an opportunity to invite business professionals to showcases from research and development of new products.

Course Curriculum