{"id":79950,"date":"2018-03-09T23:25:50","date_gmt":"2018-03-09T23:25:50","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/high-order-numerical-methods-applied-to-the-analysis-of-transport-phenomena-in-combustion\/"},"modified":"2018-03-09T23:25:50","modified_gmt":"2018-03-09T23:25:50","slug":"high-order-numerical-methods-applied-to-the-analysis-of-transport-phenomena-in-combustion","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/resolucion-de-ecuaciones-diferenciales-en-derivadas-parciales\/high-order-numerical-methods-applied-to-the-analysis-of-transport-phenomena-in-combustion\/","title":{"rendered":"High order numerical methods applied to the analysis of transport phenomena in combustion"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Miguel Hermanns <\/strong><\/h2>\n<p>Los m\u00e9todos num\u00e9ricos de alto orden se caracteriza por la propiedad de que, al igual n\u00famero de nodos, o grados de libertad, su error es mucho menor que el de los m\u00e9todos num\u00e9ricos de segundo orden. Este hecho los vuelve muy atractivos para aplicaciones tales como la ac\u00fastica y aeroac\u00fastica computacional, la predicci\u00f3n de transici\u00f3n o la simulaci\u00f3n num\u00e9rica directa dela turbulencia. Pero los m\u00e9todos num\u00e9ricos de alto orden tienden a ser num\u00e9ricamente inestables, lo cual ha obstaculizado su uso generalizado. El origen de dichas inestabilidades se atribuye a la presencia de contornos y a la manera en al que se imponen las condiciones de contorno en estos m\u00e9todos. en el presente trabajo se consigue la estabilidad num\u00e9rica de los m\u00e9todos de diferencias finitas de alto orden mediante la inhibici\u00f3n del fen\u00f3meno de runge, responsable de las fuertes oscilaciones que se observan en las interpolaciones polin\u00f3micas realizadas con nodos equiespaciados. Siguiendo la filosof\u00eda que subyace en los polinomios de chebyshev, se introduce la idea de una malla \u00f3ptima para interpolaciones polin\u00f3micas a trozos de grado q menor n. Se demuestra, que cuando q= n, la interpolaci\u00f3n polin\u00f3mica sobre nodos \u00f3ptimos coincide con la interpolaci\u00f3n de chebyshev, y por tanto los esquemas de diferencias finitas resultantes son equivalentes a los m\u00e9todos de colocaci\u00f3n de chebyshev. En el l\u00edmite opuesto, cuando q? N, se demuestra que con agrupar unos pocos nodos, del orden de o(q), es suficiente para alcanzar la deseada estabilidad del m\u00e9todo num\u00e9rico. Mediante la resoluci\u00f3n num\u00e9rica de los operadores de convecci\u00f3n-difussi\u00f3n y ac\u00fastico se muestra que esta nueva familia de m\u00e9todos de diferencias finitas es capaz de obtener soluciones num\u00e9ricamente estables para cualquier grado q? N y que dichas soluciones presentan un comportamiento transitorio correcto. Por ello se ha extendido el uso de estos m\u00e9todos num\u00e9ricos al estudio de dos problemas fluidodin\u00e1micos de combu<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>High order numerical methods applied to the analysis of transport phenomena in combustion<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 High order numerical methods applied to the analysis of transport phenomena in combustion <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Miguel Hermanns <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 16\/05\/2006<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Amable Li\u00f1an Martinez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jes\u00fas Mar\u00eda Sanz serna <\/li>\n<li> Sanchez perez Antonio  Luis (vocal)<\/li>\n<li> Higuera ant\u00f3n Francisco Jos\u00e9 (vocal)<\/li>\n<li>Antonio Crespo Martinez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Miguel Hermanns Los m\u00e9todos num\u00e9ricos de alto orden se caracteriza por la propiedad de que, al igual [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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