A doubly reduced approximation for the solution to PDE's based on a domain truncation and a reduced basis method: Application to Navier-Stokes equations
Résumé
This paper focuses on the non-intrusive reduced basis (NIRB) method called the \textit{two grids method}. It is used
for the simulation of parametric partial differential equations to reduce the associated computational costs of a
High-Fidelity code when such problems must be solved for a large number of parameter values or provide a
solution in “real time”.
As other reduced basis approaches, the “offline step” relies on the High-Fidelity method with a fine enough
grid. On the contrary, the non-intrusiveness of the original \textit{two grids method} is based on the use, in the “online
step”, of the same method with a much coarser grid, which considerably reduces the cost of this step.
We extend here this idea by further reducing the “online step” and further simplify the High-Fidelity method.
As an example of application we consider a classical fluid problem, the 2D Backward Facing Step (BFS). We
simplify the model by i) truncating the outflow part of the channel at extreme and ii) using a coarse uniform
mesh instead of refining it at the re-entrant corner, both choices that contradict what is required to get a high
fidelity representation of the flow. To accomplish this, we create two reduced bases and a deterministic process
that allows us to pass from one to the other.
Several numerical simulations illustrate the ability of this new approach.
Origine : Fichiers produits par l'(les) auteur(s)