The transport in channels, modelled by advection-diffusion-reaction equations, is fundamental is several applications in engineering and natural sciences. Unfortu- nately the numerical resolution of the model at issue is challenging with respect to the computational demanding. Thus surrogate reduced models are proposed in order to balance the best trade-off between reliability and computational efficiency. In this context HiMod (Hierarchical Model Reduction) method is optimal to deal with specific problems presenting main dynamics. It works solving separately along the direction of the main dynamic through Finite Elements and along the direction of the second dynamics through Spectral Elements. The new proposed model HiPhomε lays its basis on HiMod and applies the perturbative-homogenisation technique in order to define automatically and recursively new modal bases derived directly from the flow at issue. This let the applications to many intriguing cases, ranging from generally transport problems in pipes and channels to transport problems in porous and fractured media.
Il problema di trasporto in un canale, modellato tramite equazioni di convezione- diffusione-reazione, è fondamentale in svariati campi dell’ingegneria e delle scienze naturali. Sfortunatamente la risoluzione numerica completa di tale modello è spesso problematica per il grosso costo computazionale e l’alto numero di parametri in gioco. Modelli di riduzione vengono perciò introdotti allo scopo di bilanciare affidabilità ed efficienza. In questo ambito nasce HiMod (Hieararchical Model Reduction), ottimizzato per risolvere problemi aventi dinamiche principali, risol- vendo separatamente lungo la direzione di queste ultime con Elementi Finiti e lungo la direzione delle secondarie tramite Elementi Spettrali a basso ordine. In tal maniera si possono risolvere problemi due o tre dimensionali con costo com- putazionale equivalente a problemi uno dimensionali. Il nuovo modello proposto HiPhomε (Hieararchical Perturbation-based Model) applica l’idea perturbativa alla base dell’omogeneizzazione nel contesto di HiMod. In questo modo ottimizziamo la definizione di base modale per Elementi Spettrali, ottenendole automaticamente e ricorsivamente a partire dal campo di velocità del flusso in esame. Questo permette l’applicazione di HiPhomε in moltissimi contesti anche diversi tra loro che spaziano da il trasporto in mezzi porosi e fratturati ad, in generale, il trasporto in tubi o canali.
Hierarchical perturbation-based model reduction : applications to advection-diffusion-reaction problems
PICCARDO, STEFANO
2017/2018
Abstract
The transport in channels, modelled by advection-diffusion-reaction equations, is fundamental is several applications in engineering and natural sciences. Unfortu- nately the numerical resolution of the model at issue is challenging with respect to the computational demanding. Thus surrogate reduced models are proposed in order to balance the best trade-off between reliability and computational efficiency. In this context HiMod (Hierarchical Model Reduction) method is optimal to deal with specific problems presenting main dynamics. It works solving separately along the direction of the main dynamic through Finite Elements and along the direction of the second dynamics through Spectral Elements. The new proposed model HiPhomε lays its basis on HiMod and applies the perturbative-homogenisation technique in order to define automatically and recursively new modal bases derived directly from the flow at issue. This let the applications to many intriguing cases, ranging from generally transport problems in pipes and channels to transport problems in porous and fractured media.File | Dimensione | Formato | |
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https://hdl.handle.net/10589/146038