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• W2785944858 abstract "In this thesis we develop a method for the estimation of the flow behaviour of an incom-pressible fluid based on observations of the brightness intensity of a transported visiblesubstance which does not influence the flow. The observations are given in a subregion ofthe flow as a sequence of discrete images with in- and outflow across the image boundaries.The resulting mathematical problem is ill-posed and has to be regularised with informationof the underlying fluid flow model.We consider a constrained optimisation problem, namely the minimisation of a trackingtype data term for the brightness distribution and a regularisation term subject to asystem of weakly coupled partial differential equations. The system consists of the time-dependent incompressible Navier-Stokes equations coupled by the velocity vector field to aconvection-diffusion equation, which describes the transport of brightness patterns in theimage sequence.Due to the flow across the boundaries of the computational domain we solve a boundaryidentification problem. The usage of (strong) Dirichlet boundary controls for this purposeleads to theoretical and numerical complications, so that we will instead use Robin-typecontrols, which allow for a more convenient theoretical and numerical framework. Wewill prove well-posedness and investigate the functionality of the proposed approach bymeans of numerical examples. Furthermore, we discuss the connection to Dirichlet-controlproblems, e. g. the approximation of Dirichlet-controls by the so-called penalised Neumannmethod, which is based on the Robin-type controls for a varying penalty parameter.We will show via numerical tests that Robin-type controls are suitable for the identifi-cation of the correct fluid flow. Moreover, the examples indicate that the underlyingphysical model used for the regularisation influences the flow reconstruction process. Thusappropriate knowledge of the model is essential, e. g. the viscosity parameter. For a time-independent example we will present a heuristic, which, beside the boundary identification,automatically evaluates the viscosity in case the parameter is unknown.The developed physics-based optical flow estimation approach is finally used for the dataset of a prototypical application. The background of the application is the approximation ofhorizontal wind fields in sparsely populated areas like desert regions. A sequence of satelliteimages documenting the brightness intensity of an observable substance distributed bythe wind (e. g. dust plumes) is thereby assumed to be the only available data. Wind fieldinformation is for example needed to simulate the distribution of other, not directly observ-able, substances in the lower atmosphere. For the prototypical example we compute a highquality reconstruction of the underlying fluid flow by a (discrete) sequence of consecutivespatially distributed brightness intensities. Thereby, we compare three different models(heat equation, Stokes system and the original fluid flow model) in the reconstructionprocess and show that using as much model knowledge as possible is essential for a goodreconstruction result." @default.
• W2785944858 created "2018-02-23" @default.
• W2785944858 creator A5041916615 @default.
• W2785944858 date "2015-01-01" @default.
• W2785944858 modified "2023-09-27" @default.
• W2785944858 title "Variational Methods for the Estimation ofTransport Fields with Application to theRecovery of Physics-Based Optical FlowsAcross Boundaries" @default.
• W2785944858 doi "https://doi.org/10.11588/heidok.00018724" @default.
• W2785944858 hasPublicationYear "2015" @default.
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