Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method
A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diffusion-reaction equation in two-dimensional domains. The Local Hermitian Interpolation (LHI) method is employed for the spatial discretization and several strategies are implemented for the solution...
- Autores:
-
Bustamante Chaverra, Carlos A
Power, Henry
Florez Escobar, Whady
Hill Betancourt, Alan F
- Tipo de recurso:
- Fecha de publicación:
- 2013
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/14409
- Acceso en línea:
- http://hdl.handle.net/10784/14409
- Palabra clave:
- Radial Basis Functions
Meshless Methods
Symmetric Method
Newton Raphson
Homotopy Analysis Method
Funciones De Base Radial
Métodos Sin Malla
Método Simétrico
Newton Raphson
Método De Análisis De Homotopía
- Rights
- License
- Acceso abierto
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| dc.title.eng.fl_str_mv |
Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method |
| dc.title.spa.fl_str_mv |
Solución bidimensional sin malla de la ecuación no lineal de convección-difusión-reacción mediante el método de Interpolación Local Hermítica |
| title |
Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method |
| spellingShingle |
Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method Radial Basis Functions Meshless Methods Symmetric Method Newton Raphson Homotopy Analysis Method Funciones De Base Radial Métodos Sin Malla Método Simétrico Newton Raphson Método De Análisis De Homotopía |
| title_short |
Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method |
| title_full |
Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method |
| title_fullStr |
Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method |
| title_full_unstemmed |
Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method |
| title_sort |
Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation method |
| dc.creator.fl_str_mv |
Bustamante Chaverra, Carlos A Power, Henry Florez Escobar, Whady Hill Betancourt, Alan F |
| dc.contributor.author.spa.fl_str_mv |
Bustamante Chaverra, Carlos A Power, Henry Florez Escobar, Whady Hill Betancourt, Alan F |
| dc.contributor.affiliation.spa.fl_str_mv |
Universidad Pontificia Bolivariana University of Nottingham Universidad Pontificia Bolivariana Universidad Pontificia Bolivariana |
| dc.subject.keyword.eng.fl_str_mv |
Radial Basis Functions Meshless Methods Symmetric Method Newton Raphson Homotopy Analysis Method |
| topic |
Radial Basis Functions Meshless Methods Symmetric Method Newton Raphson Homotopy Analysis Method Funciones De Base Radial Métodos Sin Malla Método Simétrico Newton Raphson Método De Análisis De Homotopía |
| dc.subject.keyword.spa.fl_str_mv |
Funciones De Base Radial Métodos Sin Malla Método Simétrico Newton Raphson Método De Análisis De Homotopía |
| description |
A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diffusion-reaction equation in two-dimensional domains. The Local Hermitian Interpolation (LHI) method is employed for the spatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM). The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs) are employed to build the interpolation function. Unlike the original Kansa’s Method, the LHI is applied locally and the boundary and governing equation differential operators are used to obtain the interpolation function, giving a symmetric and non-singular collocation matrix. Analytical and Numerical Jacobian matrices are tested for the Newton-Raphson method and the derivatives of the governing equation with respect to the homotopy parameter are obtained analytically. The numerical scheme is verified by comparing the obtained results to the one-dimensional Burgers’ and two-dimensional Richards’ analytical solutions. The same results are obtained for all the non-linear solvers tested, but better convergence rates are attained with the Newton Raphson method in a double iteration scheme. |
| publishDate |
2013 |
| dc.date.issued.none.fl_str_mv |
2013-03-22 |
| dc.date.available.none.fl_str_mv |
2019-11-22T17:02:38Z |
| dc.date.accessioned.none.fl_str_mv |
2019-11-22T17:02:38Z |
| dc.date.none.fl_str_mv |
2013-03-22 |
| dc.type.eng.fl_str_mv |
article info:eu-repo/semantics/article publishedVersion info:eu-repo/semantics/publishedVersion |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.local.spa.fl_str_mv |
Artículo |
| status_str |
publishedVersion |
| dc.identifier.issn.none.fl_str_mv |
2256-4314 1794-9165 |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/10784/14409 |
| dc.identifier.doi.none.fl_str_mv |
10.17230/ingciecia.9.17.2 |
| identifier_str_mv |
2256-4314 1794-9165 10.17230/ingciecia.9.17.2 |
| url |
http://hdl.handle.net/10784/14409 |
| dc.language.iso.eng.fl_str_mv |
eng |
| language |
eng |
| dc.relation.isversionof.none.fl_str_mv |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1824 |
| dc.relation.uri.none.fl_str_mv |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1824 |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.local.spa.fl_str_mv |
Acceso abierto |
| rights_invalid_str_mv |
Acceso abierto http://purl.org/coar/access_right/c_abf2 |
| dc.format.none.fl_str_mv |
application/pdf |
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees |
| dc.publisher.spa.fl_str_mv |
Universidad EAFIT |
| dc.source.none.fl_str_mv |
instname:Universidad EAFIT reponame:Repositorio Institucional Universidad EAFIT |
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Ingeniería y Ciencia; Vol 9, No 17 (2013) |
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Universidad EAFIT |
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees2013-03-222019-11-22T17:02:38Z2013-03-222019-11-22T17:02:38Z2256-43141794-9165http://hdl.handle.net/10784/1440910.17230/ingciecia.9.17.2A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diffusion-reaction equation in two-dimensional domains. The Local Hermitian Interpolation (LHI) method is employed for the spatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM). The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs) are employed to build the interpolation function. Unlike the original Kansa’s Method, the LHI is applied locally and the boundary and governing equation differential operators are used to obtain the interpolation function, giving a symmetric and non-singular collocation matrix. Analytical and Numerical Jacobian matrices are tested for the Newton-Raphson method and the derivatives of the governing equation with respect to the homotopy parameter are obtained analytically. The numerical scheme is verified by comparing the obtained results to the one-dimensional Burgers’ and two-dimensional Richards’ analytical solutions. The same results are obtained for all the non-linear solvers tested, but better convergence rates are attained with the Newton Raphson method in a double iteration scheme.Se desarrolla un esquema numérico sin malla para resolver una versión genérica de la ecuación no lineal de convección-difusión-reacción en dominios bidimensionales. El método de Interpolación Hermitiana Local (LHI) se emplea para la discretización espacial y se implementan varias estrategias para la solución del sistema de ecuaciones no lineal resultante, entre ellas la iteración Picard, el método Newton Raphson y una versión truncada del Método de Análisis de Homotopía. (JAMÓN). El método LHI es una estrategia de colocación local en la que se utilizan funciones de base radial (RBF) para construir la función de interpolación. A diferencia del método original de Kansa, el LHI se aplica localmente y los operadores diferenciales de ecuación límite y gobernante se utilizan para obtener la función de interpolación, dando una matriz de colocación simétrica y no singular. Las matrices analíticas y numéricas jacobianas se prueban para el método de Newton-Raphson y las derivadas de la ecuación de gobierno con respecto al parámetro de homotopía se obtienen analíticamente. El esquema numérico se verifica comparando los resultados obtenidos con las soluciones analíticas unidimensionales de Burgers y Richards bidimensionales. Se obtienen los mismos resultados para todos los solucionadores no lineales probados, pero se obtienen mejores tasas de convergencia con el método Newton Raphson en un esquema de doble iteración.application/pdfengUniversidad EAFIThttp://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1824http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1824Copyright (c) 2013 Carlos A Bustamante Chaverra, Henry Power, Whady F Florez Escobar, Alan F Hill BetancourtAcceso abiertohttp://purl.org/coar/access_right/c_abf2instname:Universidad EAFITreponame:Repositorio Institucional Universidad EAFITIngeniería y Ciencia; Vol 9, No 17 (2013)Two-dimensional meshless solution of the non-linear convection diffusion reaction equation by the Local Hermitian Interpolation methodSolución bidimensional sin malla de la ecuación no lineal de convección-difusión-reacción mediante el método de Interpolación Local Hermíticaarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Radial Basis FunctionsMeshless MethodsSymmetric MethodNewton RaphsonHomotopy Analysis MethodFunciones De Base RadialMétodos Sin MallaMétodo SimétricoNewton RaphsonMétodo De Análisis De HomotopíaBustamante Chaverra, Carlos APower, HenryFlorez Escobar, WhadyHill Betancourt, Alan FUniversidad Pontificia BolivarianaUniversity of NottinghamUniversidad Pontificia BolivarianaUniversidad Pontificia BolivarianaIngeniería y Ciencia9172151ing.cienc.THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/6b0b293a-5224-4a46-837e-27aa91261d2e/downloadda9b21a5c7e00c7f1127cef8e97035e0MD51ORIGINAL2.pdf2.pdfTexto completo PDFapplication/pdf781573https://repository.eafit.edu.co/bitstreams/ae3228c2-f782-4f48-b9ba-935cdac1c01e/download3654522ad07b300774e6e722b5da2e28MD52articulo.htmlarticulo.htmlTexto completo HTMLtext/html374https://repository.eafit.edu.co/bitstreams/cbb4f91f-c3ba-447f-a55f-238f51061f5f/download757377fee8b37a94a6815b836318e81eMD5310784/14409oai:repository.eafit.edu.co:10784/144092020-03-02 21:07:06.723open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co |