The purpose of this work is to investigate the inf-sup stability of reduced basis (RB) method applied to parametric Stokes problem. While performing the Galerkin projection on the reduced space, the inf-sup approximation stability has always been a challenge for the RB community, even if the construction of reduced basis is done using a stable high-fidelity method. In this work we propose a new online stabilization strategy for RB approximation of parametrized Stokes problem. In this strategy, a stable high-fidelity method is used to construct the RB spaces, and then, online solution is improved by a post processing based on rectification method [8, 13, 16]. This approach involves the computation of less expensive (but less consistent) FE approximation during the online stage and hence the improvement of online solutions using a RB-based rectification method. The consistency of the RB solution is also improved. We compare this approach with existing offline-online stabilization approach presented in our earlier work [2]. All the numerical simulations are carried out using RBniCS [4, 14], an open-source reduced order modelling library, built on top of FEniCS [15].
Ali, S., Ballarin, F., Rozza, G., An Online Stabilization Method for Parametrized Viscous Flows, Reduction, Approximation, Machine Learning, Surrogates, Emulators and Simulators: RAMSES, Springer Nature Switzerland AG, Cham 2024 <<LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING>>,: 1-16. 10.1007/978-3-031-55060-7_1 [https://hdl.handle.net/10807/281976]
An Online Stabilization Method for Parametrized Viscous Flows
Ballarin, Francesco;
2024
Abstract
The purpose of this work is to investigate the inf-sup stability of reduced basis (RB) method applied to parametric Stokes problem. While performing the Galerkin projection on the reduced space, the inf-sup approximation stability has always been a challenge for the RB community, even if the construction of reduced basis is done using a stable high-fidelity method. In this work we propose a new online stabilization strategy for RB approximation of parametrized Stokes problem. In this strategy, a stable high-fidelity method is used to construct the RB spaces, and then, online solution is improved by a post processing based on rectification method [8, 13, 16]. This approach involves the computation of less expensive (but less consistent) FE approximation during the online stage and hence the improvement of online solutions using a RB-based rectification method. The consistency of the RB solution is also improved. We compare this approach with existing offline-online stabilization approach presented in our earlier work [2]. All the numerical simulations are carried out using RBniCS [4, 14], an open-source reduced order modelling library, built on top of FEniCS [15].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.