Título:
Approximation and interpolation of divergence free flows.
Otros títulos:
Coordinador:
Director:
Compilador:
Autor:
Tempone, Raúl F.
Tutor:
Oppelstrup, Jesper
Tipo de documento:
Tesis de maestría
Editor:
Palabras clave:
Incompressible flow
Mass consistent models
Inverse problems
Ill-posed problems
Regularization methods
Mass consistent models
Inverse problems
Ill-posed problems
Regularization methods
Descriptores:
Año de publicación:
1999
Contenido:
Resumen:
In many applications like meteorology, atmospheric pollution studies, eolic energy prospection, estimation of instantaneous velocity fields etc., one faces the problem of estimating a velocity field that is assumed to be incompressible. Very often the available data contains just a few and sparse velocity measurements and may be some boundary conditions imposed by solid boundaries. This inverse problem is studied here, and a new method to provide a numerical solution is presented. It is based on the Fourier transform, and allows to include the
incompressibility constraint in a simple way, leading to an unconstrained least squares formulation, usually ill-posed. The Tikhonov regularization is applied to stabilize the solution, as well as to provide some smoothness in the estimated fow. As a consequence, the numerical solution will generally approximate the measurements up to a threshold given by the size of the regularization parameter. Moreover, if the available velocity measurements come from a smooth velocity field then the numerical solution can be usually constructed using just a small number of Fourier terms. The choice of the regularization parameter is done using the L curve method,
balancing the perturbation and regularization contributions to the error. Perturbation bounds (i.e.), bounds for the condition number of the matrix from the Least Squares formulation are included. Numerical experiments with test problems and real data from the southern part of Uruguay are carried out. In addition, the results are compared with related work and the results are satisfactory.
Descripción:
Editorial:
Udelar.FI.
EN:
Financiadores:
Citación:
Tempone, R. Approximation and interpolation of divergence free flows [en línea] Tesis de maestría. Montevideo : Udelar. FI, 1999.
Citación:
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Documento del Gobiberno:
URI:
https://hdl.handle.net/20.500.12008/24377
ISBN:
e-ISBN:
ISSN:
1688-2792
ISMN:
Otros identificadores:
Título Obtenido:
Magíster en Ingeniería (Ingeniería Matemática)
Facultad o Servicio que otorga el Título:
Universidad de la República (Uruguay). Facultad de Ingeniería.
Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| Tem99.pdf | Tesis de maestría | 5.99 MB | Adobe PDF |