Advanced Numerical Methods and Simulation
Syllabus
The course covers several numerical methods to solve time-dependent partial differential equations using finite elements and stabilisation. Advanced methods for turbulence modeling, multiphase flows, complex fluid flows and aerothermal modelling of complex systems will be given. Finally, the course will be completed by error estimator needed for anisotropic parallel mesh adaptation.
Schedule
Times: AM 09-12, PM 13:30-16:30
Location: Room I/E102 or I/E201b – Zoom sessions will be communicated 24h before each lecture.
| Week 02 | Location | |
| 9. January | I/E201B | E. Hachem “Stabilized finite elements for the convection–diffusion–reaction equation” (PM) |
| 11. January | I/E102 | |
| Week 03 | ||
| 16. January | I/E201B | R. Valette “Some models and resolution methods for complex fluids flows” (AM+PM) Lectures |
| 18. January | I/E102 | J. Viquerat “Coupling machine learning with CFD” (AM+PM) Lecture + Lab |
| Week 04 | ||
| 23. January | I/E201B | |
| 25. January | I/E201B | P. Meliga “Hydrodynamic instabilities and the route to chaos” (AM) A. Pereira “Soft matter in flow” (PM) |
| Week 05 | ||
| 30. January | I/E102 | F. Pigeonneau “Natural convection in a square cavity: Scaling and numerical analysis” (AM+PM) Lecture + Lab |
| Week 07 | ||
| 12. February | I/E201B | A. Larcher “Numerical Solution of PDEs with Finite Element Methods: a quick re-introduction on theory and practice” (AM+PM) (Finite Element Methods, Estimates, Mixed problems) |
| 13. February | I/E201B | T. Coupez “Anisotropic mesh adaptation” (AM) |
| 16. February | I/E201B | E. Hachem “Stabilized Finite Elements for convection-diffusion and Navier–Stokes equations” (PM) |