Reference : Hi-POD solution of parametrized fluid dynamics problems: preliminary results

	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/29014

Title :	Hi-POD solution of parametrized fluid dynamics problems: preliminary results
Language :	English
Author, co-author :	Baroli, Davide* [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
	Cova, Maria Cristina* [Mathematics Department > Politecnico di Milano > > MsC.]
	Perotto, Simona* [Politecnico di Milano > Mathematics Department > > Full Professor in Numerical Analysis]
	Sala, Lorenzo* [Politecnico di Milano > Mathematics Department > > PhD student at University of Strasburg]
	Veneziani, Alessandro* [Emory University, Atlanta, GA USA. > Department of Mathematics and Computer Science > > Professor]
	* These authors have contributed equally to this work.
Publication date :	2018
Journal title :	MS&A series
Publisher :	Springer
Volume :	MS&A series
Issue/season :	3
Special issue title :	Model Reduction of Parametrized Systems III
Peer reviewed :	Yes
Audience :	International
ISSN :	9783319587868
Keywords :	[en] model reduction ; surrogate model ; fluid dynamics
Abstract :	[en] Numerical modeling of fluids in pipes or network of pipes (like in the circulatory system) has been recently faced with new methods that exploit the specific nature of the dynamics, so that a one dimensional axial mainstream is enriched by local secondary transverse components [4, 16, 18]. These methods - under the name of Hi-Mod approximation - construct a solution as a finite element axial discretization, completed by a spectral approximation of the transverse dynamics. It has been demonstrated that Hi-Mod reduction significantly accelerates the computations without com- promising the accuracy. In view of variational data assimilation procedures (or, more in general, control problems), it is crucial to have efficient model reduction techniques to rapidly solve, for instance, a parametrized problem for several choices of the parameters of interest. In this work, we present some preliminary results merging Hi-Mod techniques with a classical Proper Orthogonal Decomposition (POD) strategy. We name this new approach as Hi-POD model reduction. We demonstrate the efficiency and the reliability of Hi-POD on multiparameter advection-diffusion-reaction problems as well as on the incompressible Navier-Stokes equations, both in a steady and in an unsteady setting.
Funders :	National Science Foundation - NSF
Name of the research project :	Hierarchical model reduction techniques for incompressible fluid dynamics and fluid-structure interaction problems- DMS-1419060
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/29014
DOI :	10.1007/978-3-319-58786-8_15

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