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Reconstruction of velocity data, using the viscous Burgers' equation and adjoint optimization
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Biomedical Engineering. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-5526-2399
(English)Manuscript (preprint) (Other academic)
Abstract [en]

For a given field u*, a field u governed by a nonlinear partial differential equation and minimizing ||u - u*||2 is determined. The initial condition is used as control variable and the gradient for the minimization is based on adjoint technique. Continuous and discrete gradient formulations are compared. The method handles missing as well as noisy data.

Keyword [en]
adjoint technique, data reconstruction, optimal flow control, optimization, uncertain velocity data
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-100374OAI: diva2:661687
Available from: 2013-11-04 Created: 2013-11-04 Last updated: 2016-03-14
In thesis
1. Reconstruction of velocity data using adjoint optimization
Open this publication in new window or tab >>Reconstruction of velocity data using adjoint optimization
2004 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In many application areas there is a growing interest in data assimilation or data reconstruction. Data assimilation is a process for integrating observed or measured data into a physical model. The problem originates from a vast array of different topics: traditionally in metereological and oceanographic modelling, and recently from non-invasive medical measurement devices such as magnetic resonance imaging. The measured data may contain inaccurancies and random noise, given with low spatial and/or temporal resolution.

This thesis presents a method for solving reconstruction problems in fluid dynamics using optimal control theory. The problem considered here includes a known partial differential equation and some spatially and temporarily sparsely distributed data with an unknown initial state. From a given velocity field uδ, a flow field u is determined which satisfies a given system of partial differential equations and minimizes || u - u*|| L2. The function u(x,t) is known at the boundary and the initial condition u0(x) is used as design variable. The optimization problem is solved using adjoint formulation.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2004. 8 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1096
National Category
urn:nbn:se:liu:diva-23162 (URN)2566 (Local ID)91-7373-969-3 (ISBN)2566 (Archive number)2566 (OAI)
2004-05-25, Glashuset, Hus B, Linköpings universitet, Linköpings, 13:15 (Swedish)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-11-04

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