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1. Noronha Neto, Celso de Carvalho. Matriz de massa de ordem elevada, dispersão de velocidades e reflexões espúrias.

Degree: PhD, Estruturas, 2008, University of São Paulo

O assunto principal deste trabalho é qualificar, quantificar e implementar o comportamento numérico de estruturas discretizadas através do método dos elementos finitos. Serão abordados apenas os elementos lineares unidimensionais dinâmicos, porém a aplicabilidade da formulação proposta pode se estender para elementos bi e tridimensionais lineares dinâmicos. Inicia-se com uma introdução ao tema. Com certo desenvolvimento matemático, pode-se isolar analiticamente a parcela relacionada ao erro numérico. Elevando a ordem do erro de truncamento, obtém-se precisão elevada na resposta numérica. Inspirado no integrador temporal de Newmark, projetam-se elementos que apresentam estabilidade incondicional para os chamados efeitos espúrios. O efeito evanescente é um fenômeno espúrio onde a onda se propaga ao longo da estrutura acompanhada de um amortecimento puramente numérico ao longo do domínio do espaço. Outro efeito analisado é a reflexão espúria. Quando dois elementos adjacentes têm comprimentos diferentes, surge uma onda de reflexão (ou duas, no caso do elemento de viga) na interface deles. Tal onda, também de origem puramente matemática, existe devido à diferença entre as massas e as rigidezes absolutas dos elementos envolvidos, independente do fato de que eles tenham as mesmas características físicas. A relação entre o incremento de tempo e o período de oscilação é convenientemente empregada como principal parâmetro para quantificar a discretização no domínio temporal. No domínio do espaço, a relação empregada é entre o comprimento do elemento e o comprimento de onda.

The main subject of this work is to qualify, quantify and implement the numerical behavior of discrete structures through the finite element method. It will be investigated only the dynamic onedimensional linear elements, but the applicability of the proposed formulation can be extended to the bi and tri-dimensional cases. It begins with an introduction to the theme. With some mathematical development, the related numerical error can be isolated analytically. Once the truncation error is isolate, a high precision numerical response is obtained. Inspired in the Newmark time integrator, unconditionally stable elements for spurious effects are idealized. The evanescent effect is a spurious phenomenon where the wave propagates along the structure subjected to a numerical damping in the spatial domain. Another effect analyzed here is the spurious wave reflection. When two adjacent elements have different lengths, a reflected wave exists (two waves for the beam element) at their interface. This wave, which meaning is purely mathematical, exists due to the difference of their absolute mass and stiffness between the finite elements involved, even when both elements have the same physical properties. The rate between the time increment and the period of oscillation is conveniently employed as the main parameter to quantify the time discretization. In the spatial domain, the used parameter is the relation between the element and the wave length.

Advisors/Committee Members: Laier, José Elias.

Subjects/Keywords: Dinâmica estrutural; Elementos finitos; Evanescent waves; Finite element; Numerical precision; Ondas espúrias; Ondas evanescentes; Precisão numérica; Spurious wave reflections; Structural dynamics; Timoshenko; Timoshenko

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Noronha Neto, C. d. C. (2008). Matriz de massa de ordem elevada, dispersão de velocidades e reflexões espúrias. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/18/18134/tde-23092008-091215/ ;

Chicago Manual of Style (16th Edition):

Noronha Neto, Celso de Carvalho. “Matriz de massa de ordem elevada, dispersão de velocidades e reflexões espúrias.” 2008. Doctoral Dissertation, University of São Paulo. Accessed September 28, 2020. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-23092008-091215/ ;.

MLA Handbook (7th Edition):

Noronha Neto, Celso de Carvalho. “Matriz de massa de ordem elevada, dispersão de velocidades e reflexões espúrias.” 2008. Web. 28 Sep 2020.

Vancouver:

Noronha Neto CdC. Matriz de massa de ordem elevada, dispersão de velocidades e reflexões espúrias. [Internet] [Doctoral dissertation]. University of São Paulo; 2008. [cited 2020 Sep 28]. Available from: http://www.teses.usp.br/teses/disponiveis/18/18134/tde-23092008-091215/ ;.

Council of Science Editors:

Noronha Neto CdC. Matriz de massa de ordem elevada, dispersão de velocidades e reflexões espúrias. [Doctoral Dissertation]. University of São Paulo; 2008. Available from: http://www.teses.usp.br/teses/disponiveis/18/18134/tde-23092008-091215/ ;


INP Toulouse

2. Vanharen, Julien. High-order numerical methods for unsteady flows around complex geometries : Méthodes numériques d'ordre élevé pour des écoulements instationnaires autour de géométries complexes.

Degree: Docteur es, Dynamique des fluides, 2017, INP Toulouse

Dans ce travail, on s'intéresse aux méthodes numériques d'ordre élevé pour des écoulements instationnaires autour de géométries complexes. On commence par analyser l'approche hybride pour la méthode industrielle des Volumes Finis à l'ordre faible. Cela consiste à calculer en même temps sur des maillages structurés et non structurés avec des schémas numériques dédiés. Les maillages structurés et non structurés sont ensuite couplés par un raccord non conforme. Ce dernier est analysé en détails avec une attention particulière pour des écoulements instationnaires. On montre qu'un traitement dédié à l'interface empêche la réflexion d'ondes parasites. De plus, l'approche hybride est validée sur plusieurs cas académiques à la fois pour les flux convectifs et pour les flux diffusifs. L'extension de cette approche hybride à l'ordre élevé est limitée par l'efficacité des schémas non structurés d'ordre élevé en terme de temps de calcul. C'est pourquoi une nouvelle approche est explorée : la méthode des différences spectrales. Un nouveau cadre est spécialement développé pour réaliser l'analyse spectrale des méthodes spectrales discontinues. La méthode des différences spectrales semble être une alternative viable en terme de temps de calcul et de nombre de points par longueur d'onde nécessaires à une application donnée pour capturer la physique de l'écoulement.

This work deals with high-order numerical methods for unsteady flows around complex geometries. In order to cope with the low-order industrial Finite Volume Method, the proposed technique consists in computing on structured and unstructured zones with their associated schemes: this is called a hybrid approach. Structured and unstructured meshes are then coupled by a nonconforming grid interface. The latter is analyzed in details with special focus on unsteady flows. It is shown that a dedicated treatment at the interface avoids the reflection of spurious waves. Moreover, this hybrid approach is validated on several academic test cases for both convective and diffusive fluxes. The extension of this hybrid approach to high-order schemes is limited by the efficiency of unstructured high-order schemes in terms of computational time. This is why a new approach is explored: The Spectral Difference Method. A new framework is especially developed to perform the spectral analysis of Spectral Discontinuous Methods. The Spectral Difference Method seems to be a viable alternative in terms of computational time and number of points per wavelength needed for a given application to capture the flow physics.

Advisors/Committee Members: Puigt, Guillaume (thesis director).

Subjects/Keywords: Volume Finis; Raccords Non Conformes; Approche Hybride; Schémas Non Structurés d'Ordre Elevé; Ondes Parasites; Différences Spectrales; Analyse Spectrale; Finite Volume; Nonconforming Grid Interface; Hybrid Approach; High-Order Unstructured Schemes; Spurious Waves; Spectral Difference; Spectral Analysis; 530

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Vanharen, J. (2017). High-order numerical methods for unsteady flows around complex geometries : Méthodes numériques d'ordre élevé pour des écoulements instationnaires autour de géométries complexes. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2017INPT0030

Chicago Manual of Style (16th Edition):

Vanharen, Julien. “High-order numerical methods for unsteady flows around complex geometries : Méthodes numériques d'ordre élevé pour des écoulements instationnaires autour de géométries complexes.” 2017. Doctoral Dissertation, INP Toulouse. Accessed September 28, 2020. http://www.theses.fr/2017INPT0030.

MLA Handbook (7th Edition):

Vanharen, Julien. “High-order numerical methods for unsteady flows around complex geometries : Méthodes numériques d'ordre élevé pour des écoulements instationnaires autour de géométries complexes.” 2017. Web. 28 Sep 2020.

Vancouver:

Vanharen J. High-order numerical methods for unsteady flows around complex geometries : Méthodes numériques d'ordre élevé pour des écoulements instationnaires autour de géométries complexes. [Internet] [Doctoral dissertation]. INP Toulouse; 2017. [cited 2020 Sep 28]. Available from: http://www.theses.fr/2017INPT0030.

Council of Science Editors:

Vanharen J. High-order numerical methods for unsteady flows around complex geometries : Méthodes numériques d'ordre élevé pour des écoulements instationnaires autour de géométries complexes. [Doctoral Dissertation]. INP Toulouse; 2017. Available from: http://www.theses.fr/2017INPT0030


INP Toulouse

3. Muscat, Laurent. Coupling of time integration schemes for compressible unsteady flows : Couplage de schémas temporels pour la simulation des écoulements compressibles instationnaires.

Degree: Docteur es, Dynamique des fluides, 2019, INP Toulouse

Dans ce travail, on s'intéresse au développement d'une méthode hybride qui couple spatialement les schémas d'intégration temporelle explicite et implicite. Afin de répondre aux contraintes du solveur industriel FLUSEPA, les schémas explicite Heun et implicite Crank-Nicolson ont été hybridés via un paramètre de transition : l'approche mise en place est appelée schéma AION. Cette dernière est étudiée en détails avec une attention particulière sur son comportement spectral et sa capacité à maintenir l'ordre de précision. On montre que le traitement hybride a d'intéressants comportements dissipatif et dispersif tout en empêchant la réflexion d'ondes parasites et en maintenant la précision attendue. De plus, l'approche hybride est validée sur plusieurs cas académiques à la fois pour les flux convectifs et pour les flux diffusifs. Et comme espéré, la méthode est plus intéressante en terme de temps de calcul que les méthodes standards d'intégration temporelle. Pour l'extension de cette approche à la méthode temporelle adaptative présente dans FLUSEPA, il a été nécessaire d'améliorer le traitement qui permet à la méthode d’être conservative tout en obtenant des propriétés spectrales acceptables. Finalement l'approche hybride a été aussi étendue pour la modélisation RANS/LES de la turbulence avec des temps de calcul intéressants tout en capturant la physique de l'écoulement

This work deals with the design of a hybrid time integrator that couples spatially explicit and implicit time integrators. In order to cope with the industrial solver of Ariane Group called FLUSEPA, the explicit scheme of Heun and the implicit scheme of Crank-Nicolson are hybridized using the transition parameter : the whole technique is called AION time integration. The latter is studied into details with special focus on spectral behaviour and on its ability to keep the accuracy. It is shown that the hybrid technique has interesting dissipation and dispersion properties while maintaining precision and avoiding spurious waves. Moreover, this hybrid approach is validated on several academic test cases for both convective and diffusive fluxes. And as expected the method is more interesting in term of computational time than standard time integrators. For the extension of this hybrid approach to the temporal adaptive method implemented in FLUSEPA, it was necessary to improve some treatments in order to maintain conservation and acceptable spectral properties. Finally the hybrid time integration was also applied to a RANS/LES turbulent test case with interesting computational time while capturing the flow physics.

Advisors/Committee Members: Puigt, Guillaume (thesis director), Montagnac, Marc (thesis director).

Subjects/Keywords: Volumes Finis; Intégration temporelle hybride; Analyse Spectrale spatio-temporelle; Ondes Parasites; Méthode temporelle adaptative; Ecoulement compressible et instationnaire; Finite Volume; Hybrid time integration; Space-time spectral analysis; Spurious Waves; Temporal adaptive method; Compressible unsteady flows

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Muscat, L. (2019). Coupling of time integration schemes for compressible unsteady flows : Couplage de schémas temporels pour la simulation des écoulements compressibles instationnaires. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2019INPT0010

Chicago Manual of Style (16th Edition):

Muscat, Laurent. “Coupling of time integration schemes for compressible unsteady flows : Couplage de schémas temporels pour la simulation des écoulements compressibles instationnaires.” 2019. Doctoral Dissertation, INP Toulouse. Accessed September 28, 2020. http://www.theses.fr/2019INPT0010.

MLA Handbook (7th Edition):

Muscat, Laurent. “Coupling of time integration schemes for compressible unsteady flows : Couplage de schémas temporels pour la simulation des écoulements compressibles instationnaires.” 2019. Web. 28 Sep 2020.

Vancouver:

Muscat L. Coupling of time integration schemes for compressible unsteady flows : Couplage de schémas temporels pour la simulation des écoulements compressibles instationnaires. [Internet] [Doctoral dissertation]. INP Toulouse; 2019. [cited 2020 Sep 28]. Available from: http://www.theses.fr/2019INPT0010.

Council of Science Editors:

Muscat L. Coupling of time integration schemes for compressible unsteady flows : Couplage de schémas temporels pour la simulation des écoulements compressibles instationnaires. [Doctoral Dissertation]. INP Toulouse; 2019. Available from: http://www.theses.fr/2019INPT0010

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