The boundary element dual reciprocity method : multidomain approach for solving 3D potential problems

The Dual Reciprocity Method (DRM) is a BEM technique to approach domain dominant problems without loosing the boundary-only nature of the BEM. For this kind of problems, domain integrals are sometimes introduced in the integral formulation. The DRM converts the domain integrals into boundary integra...

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Detalles Bibliográficos
Autor principal: Natalini, Bruno
Otros Autores: Popov, Viktor
Formato: Tesis doctoral
Lenguaje:Inglés
Publicado: University of Wales. Wessex Institute of Technology 2024
Materias:
Dual reciprocity method
Multidomain approach
3D potential
Acceso en línea:http://repositorio.unne.edu.ar/handle/123456789/56232
Aporte de:
RIUNNE - Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE) de Universidad Nacional del Nordeste
id I48-R184-123456789-56232
record_format dspace
spelling I48-R184-123456789-562322024-10-29T14:21:00Z The boundary element dual reciprocity method : multidomain approach for solving 3D potential problems Natalini, Bruno Popov, Viktor Dual reciprocity method Multidomain approach 3D potential The Dual Reciprocity Method (DRM) is a BEM technique to approach domain dominant problems without loosing the boundary-only nature of the BEM. For this kind of problems, domain integrals are sometimes introduced in the integral formulation. The DRM converts the domain integrals into boundary integrals by means of approximation functions. The DRM is general and the number of applications solved using the procedure has been increasing in the literature since early 90s. However the DRM faces a serious drawback when applied to large problems: the resulting system of equations is dense and frequently ill-conditioned. A way to overcome this inconvenient feature is by using domain subdivision in the limiting case when the resulting internal mesh looks like a finite element grid. This technique is known as the Dual Reciprocity Method - Multi Domain approach (DRM-MD). The DRM-MD produces sparse and well-conditioned system of equations. It has been successfully applied to a variety of linear and non-linear fluid dynamics problems in 2D domains and showed good performance. The extension of the procedure to 3D cases, and especially to large 3D problems, is not straightforward since factors such as continuity of the elements, DRM approximation function, scaling, number of internal DRM nodes, etc., which largely affect the performance of the code, need to be selected. In this thesis, several schemes were tested in order to have an insight on 3D DRMMD implementation. A set of codes using quadratic tetrahedrons to discretize the domain was produced and ten DRM approximation functions, five globally supported and five compactly supported Radial Basis Functions (RBF), were tested for both Poisson and steady-state advection-diffusion problems using dis-continuous elements. Compactly supported RBFs showed the highest accuracy, while the augmented thin plate splines (ATPS) showed the highest consistency in terms of accuracy and convergence for the two examples considered. A problem for implementation of the compactly supported RBFs is the lack of guidelines in choosing the size of the support, which showed to have large influence on the accuracy and convergence when these types of RBFs are used. The ATPS showed satisfactory accuracy and since its use does not involve any extra parameters, at the moment it is this function the choice of the author of this thesis for use in the DRMMD. Besides, the effect of scaling and internal DRM nodes were tested using both continuous and discontinuous elements. Results showed that scaling must be always considered to obtain an optimum performance of the code. Internal DRM nodes improve the accuracy of the codes though they are not as important as in the classical single-domain DRM. The thesis includes a few contributions on computational implementation of the DRM-MD, among them, a general assembly procedure and an alternative way to represent partial derivatives. Finally, the simulation of the transport of a pollutant disposed in an underground repository under different scenarios, which is a large case, and a feasibility study of flow in unsaturated media, which is a strongly nonlinear case, are presented and discussed. The results presented here show that the iii DRM-MD is as versatile and efficient when applied to problems defined in 3D domains as it is when solving 2D problems. 2024-10-29T12:42:02Z 2024-10-29T12:42:02Z 2005-10 Tesis doctoral Natalini, Bruno, 2005. The boundary element dual reciprocity method : multidomain approach for solving 3D potential. Tesis doctoral. Reino Unido: University of Wales. http://repositorio.unne.edu.ar/handle/123456789/56232 eng openAccess http://creativecommons.org/licenses/by-nc-nd/2.5/ar/ application/pdf p. 173 application/pdf University of Wales. Wessex Institute of Technology
institution Universidad Nacional del Nordeste
institution_str I-48
repository_str R-184
collection RIUNNE - Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)
language Inglés
topic Dual reciprocity method
Multidomain approach
3D potential
spellingShingle Dual reciprocity method
Multidomain approach
3D potential
Natalini, Bruno
The boundary element dual reciprocity method : multidomain approach for solving 3D potential problems
topic_facet Dual reciprocity method
Multidomain approach
3D potential
description The Dual Reciprocity Method (DRM) is a BEM technique to approach domain dominant problems without loosing the boundary-only nature of the BEM. For this kind of problems, domain integrals are sometimes introduced in the integral formulation. The DRM converts the domain integrals into boundary integrals by means of approximation functions. The DRM is general and the number of applications solved using the procedure has been increasing in the literature since early 90s. However the DRM faces a serious drawback when applied to large problems: the resulting system of equations is dense and frequently ill-conditioned. A way to overcome this inconvenient feature is by using domain subdivision in the limiting case when the resulting internal mesh looks like a finite element grid. This technique is known as the Dual Reciprocity Method - Multi Domain approach (DRM-MD). The DRM-MD produces sparse and well-conditioned system of equations. It has been successfully applied to a variety of linear and non-linear fluid dynamics problems in 2D domains and showed good performance. The extension of the procedure to 3D cases, and especially to large 3D problems, is not straightforward since factors such as continuity of the elements, DRM approximation function, scaling, number of internal DRM nodes, etc., which largely affect the performance of the code, need to be selected. In this thesis, several schemes were tested in order to have an insight on 3D DRMMD implementation. A set of codes using quadratic tetrahedrons to discretize the domain was produced and ten DRM approximation functions, five globally supported and five compactly supported Radial Basis Functions (RBF), were tested for both Poisson and steady-state advection-diffusion problems using dis-continuous elements. Compactly supported RBFs showed the highest accuracy, while the augmented thin plate splines (ATPS) showed the highest consistency in terms of accuracy and convergence for the two examples considered. A problem for implementation of the compactly supported RBFs is the lack of guidelines in choosing the size of the support, which showed to have large influence on the accuracy and convergence when these types of RBFs are used. The ATPS showed satisfactory accuracy and since its use does not involve any extra parameters, at the moment it is this function the choice of the author of this thesis for use in the DRMMD. Besides, the effect of scaling and internal DRM nodes were tested using both continuous and discontinuous elements. Results showed that scaling must be always considered to obtain an optimum performance of the code. Internal DRM nodes improve the accuracy of the codes though they are not as important as in the classical single-domain DRM. The thesis includes a few contributions on computational implementation of the DRM-MD, among them, a general assembly procedure and an alternative way to represent partial derivatives. Finally, the simulation of the transport of a pollutant disposed in an underground repository under different scenarios, which is a large case, and a feasibility study of flow in unsaturated media, which is a strongly nonlinear case, are presented and discussed. The results presented here show that the iii DRM-MD is as versatile and efficient when applied to problems defined in 3D domains as it is when solving 2D problems.
author2 Popov, Viktor
author_facet Popov, Viktor
Natalini, Bruno
format Tesis doctoral
author Natalini, Bruno
author_sort Natalini, Bruno
title The boundary element dual reciprocity method : multidomain approach for solving 3D potential problems
title_short The boundary element dual reciprocity method : multidomain approach for solving 3D potential problems
title_full The boundary element dual reciprocity method : multidomain approach for solving 3D potential problems
title_fullStr The boundary element dual reciprocity method : multidomain approach for solving 3D potential problems
title_full_unstemmed The boundary element dual reciprocity method : multidomain approach for solving 3D potential problems
title_sort boundary element dual reciprocity method : multidomain approach for solving 3d potential problems
publisher University of Wales. Wessex Institute of Technology
publishDate 2024
url http://repositorio.unne.edu.ar/handle/123456789/56232
work_keys_str_mv AT natalinibruno theboundaryelementdualreciprocitymethodmultidomainapproachforsolving3dpotentialproblems
AT natalinibruno boundaryelementdualreciprocitymethodmultidomainapproachforsolving3dpotentialproblems
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