Mathematics

In this talk I will discuss the stabilization techniques for parametrized viscous flows in a reduced basis setting.  Offline-online computational splitting is implemented and offline-only, offline-online stabilization are compared (as well as without stabilization approach). Different test cases are illustrated and several stabilization classical approaches  (SUPG, GLS, Brezzi-Pitkaranta, Franca, Hughes, etc) are recast into a parametric reduced order setting. This approach is then compared with the other supremizer options to guarantee the approximation stability by lifting the corresponding parametric inf-sup constant. The goal is two-fold: to guarantee stable parametrized viscous flows with increasing Reynolds numbers and to guarantee online computational savings by reducing the dimension of the online reduced basis system.