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Reduced basis method for the Smagorinsky model


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Opened Access Reduced basis method for the Smagorinsky model
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Author: Chacón Rebollo, Tomás
Delgado Ávila, Enrique
Gómez Mármol, María Macarena
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2016
Published in: Recent developments in numerical methods for model reduction (2016),
Document type: Presentation
Abstract: We present a reduced basis Smagorinsky model. This model includes a non-linear eddy diffusion term that we have to treat in order to solve efficiently our reduced basis model. We approximate this non-linear term using the Empirical Interpolation Method, in order to obtain a linearised decomposition of the reduced basis Smagorinsky model. The reduced basis Smagorinsky model is decoupled in a Online/Offline procedure. First, in the Offline stage, we construct hierarchical bases in each iteration of the Greedy algorithm, by selecting the snapshots which have the maximum a posteriori error estimation value. To assure the Brezzi inf-sup condition on our reduced basis space, we have to define a supremizer operator on the pressure solution, and enrich the reduced velocity space. Then, in the Online stage, we are able to compute a speedup solution of our problem, with a good accuracy.
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