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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Numerical simulation of compressible gas flow coupled to heat conduction in two space dimensions

Korneeva, Daria Y. 23 June 2011
The current thesis studies a model of two dimensional convection of an ideal gas in a rectangular domain having walls of finite thickness. The temperature outside of walls is considered constant. Heat exchange between walls and outside/inside air is computed using Newton's law of cooling. Heat transfer inside walls is modelled with the heat equation. The mathematical model inside enclosure involves Navier-Stokes equations coupled with equation of state for gas. The model is numerically studied using the method of large particles. One of the main goals of the current thesis was to develop a software in C# language for numerical solution of the above-described model. Physically meaningful results, including stream lines and distribution of parameters of gas and temperature inside solid walls were obtained.
2

Numerical simulation of compressible gas flow coupled to heat conduction in two space dimensions

Korneeva, Daria Y. 23 June 2011 (has links)
The current thesis studies a model of two dimensional convection of an ideal gas in a rectangular domain having walls of finite thickness. The temperature outside of walls is considered constant. Heat exchange between walls and outside/inside air is computed using Newton's law of cooling. Heat transfer inside walls is modelled with the heat equation. The mathematical model inside enclosure involves Navier-Stokes equations coupled with equation of state for gas. The model is numerically studied using the method of large particles. One of the main goals of the current thesis was to develop a software in C# language for numerical solution of the above-described model. Physically meaningful results, including stream lines and distribution of parameters of gas and temperature inside solid walls were obtained.
3

Inverse source problems and controllability for the stokes and navier-stokes equations

Montoya Zambrano, Cristhian David January 2016 (has links)
Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática / This thesis is focused on the Navier{Stokes system for incompressible uids with either Dirichlet or nonlinear Navier{slip boundary conditions. For these systems, we exploit some ideas in the context of the control theory and inverse source problems. The thesis is divided in three parts. In the rst part, we deal with the local null controllability for the Navier{Stokes system with nonlinear Navier{slip conditions, where the internal controls have one vanishing component. The novelty of the boundary conditions and the new estimates with respect to the pressure term, has allowed us to extend previous results on controllability for the Navier{ Stokes system. The main ingredients to build our result are the following: a new regularity result for the linearized system around the origin, and a suitable Carleman inequality for the adjoint system associated to the linearized system. Finally, xed point arguments are used in order to conclude the proof. In the second part, we deal with an inverse source problem for the N- dimensional Stokes system from local and missing velocity measurements. More precisely, our main result establishes a reconstruction formula for the source F(x; t) = (t)f(x) from local observations of N ����� 1 components of the velocity. We consider that f(x) is an unknown vectorial function, meanwhile (t) is known. As a consequence, the uniqueness is achieved for f(x) in a suitable Sobolev space. The main tools are the following: connection between null controllability and inverse problems throughout a result on null controllability for the N- dimensional Stokes system with N ����� 1 scalar controls, spectral analysis of the Stokes operator and Volterra integral equations. We also implement this result and present several numerical experiments that show the feasibility of the proposed recovering formula. Finally, the last chapter of the thesis presents a partial result of stability for the Stokes system when we consider a source F(x; t) = R(x; t)g(x), where R(x; t) is a known vectorial function and g(x) is unknown. This result involves the Bukhgeim-Klibanov method for solving inverse problems and some topics in degenerate Sobolev spaces.
4

Contrôle frontière des équations de Navier-Stokes / Boundary control of the Navier Stokes equations

Ngom, Evrad Marie Diokel 04 July 2014 (has links)
Cette thèse est consacrée à l'étude de problèmes de stabilisation exponentielle par retour d'état ou "feedback" des équations de Navier-Stokes dans un domaine borné Ω ⊂ Rd, d = 2 ou 3. Le cas d'un contrôle localisé sur la frontière du domaine est considéré. Le contrôle s'exprime en fonction du champ de vitesse à l'aide d'une loi de feedback non-linéaire. Celle-ci est fournie grâce aux techniques d'estimation a priori via la procédure de Faedo-Galerkin laquelle consiste à construire une suite de solutions approchées en utilisant une base de Galerkin adéquate. Cette loi de feedback assure la décroissance exponentielle de l'énergie du problème discret correspondant et grâce au résultat de compacité, nous passons à la limite dans le système satisfait par les solutions approchées. Le chapitre 1 étudie le problème de stabilisation des équations de Navier- Stokes autour d'un état stationnaire donné, tandis que le chapitre 2 examine le problème de stabilisation autour d'un état non-stationnaire prescrit. Le chapitre 3 est consacré à l'étude de la stabilisation du problème de Navier-Stokes avec des conditions aux bords mixtes (Dirichlet- Neumann) autour d'un état d'équilibre donné. Enfin, nous présentons dans le chapitre 4, des résultats numériques dans le cas d'un écoulement autour d'un obstacle circulaire / In this thesis we study the exponential stabilization of the two and three-dimensional Navier- Stokes equations in a bounded domain Ω, by means of a boundary control. The Control is expressed in terms of the velocity field by using a non-linear feedback law. In order to determine a feedback law, we consider an extended system coupling the Navier-Stokes equations with an equation satisfied by the control on the domain boundary. While most traditional approaches apply a feedback controller via an algebraic Riccati equation, the Stokes-Oseen operator or extension operators, a Galerkin method is proposed instead in this study. The Galerkin method permits to construct a stabilizing boundary control and by using energy a priori estimation technics, the exponential decay is obtained. A compactness result then allows us to pass to the limit in the nonlinear system satisfied by the approximated solutions. Chapter 1 deals with the stabilization problem of the Navier-Stokes equations around a given steady state, while Chapter 2 examines the stabilization problem around a prescribed non-stationary state. Chapter 3 is devoted to the stabilization of the Navier-Stokes problem with mixed-boundary conditions (Dirichlet-Neumann), around to a given steady-state. Finally, we present in Chapter 4, numerical results in the case of a flow around a circular obstacle
5

Die Anwendung der hyperkomplexen Funktionentheorie auf die Lösung partieller Differentialgleichungen

Kähler, Uwe 29 September 1998 (has links) (PDF)
In der vorliegenden Arbeit wird die Methode der Anwendung der hyperkomplexen Funktionentheorie zur Behandlung partieller Differentialgleichungen über beschränkten Gebieten unter Benutzung einer orthogonalen Zerlegung des Raumes L_2(U) verallgemeinert. Zum einen kann diese Zerlegung als direkte Zerlegung über dem Raum L_p(G),p>1, verallgemeinert werden, was die Untersuchung partieller Differentialgleichungen über allgemeinen Sobolev-Räumen W_p^k(G),p>1,k natürliche Zahl, ermöglicht. Dies wird am Beispiel des Stokes-Problems demonstriert. Zum anderen wird ein modifizierter Cauchy-Kern über unbeschränkten Gebieten eingeführt, deren Komplement eine nichtleere offene Menge enthält. Grundlegende Resultate der Cliffordanalysis über beschränkten Gebieten werden auf diese Situation verallgemeinert und eine orthogonale Zerlegung des Raumes L_2(G) bewiesen. Diese Resultate werden im weiteren dazu benutzt, das stationäre Stokes- bzw. Navier-Stokes-Problem in dem allgemeinen Fall eines unbeschränkten Gebietes zu untersuchen. Im weiteren wird gezeigt, dass sich die entwickelten Methoden auch auf partielle Differentialgleichungen höherer Ordnung anwenden lassen. Dies wird am Beispiel der biharmonischen Gleichung mit Randbedingungen, die Komponenten in Normalenrichtung und tangentieller Richtung besitzen, demonstriert. Am Ende beschäftigen wir uns mit der Verallgemeinerung der komplexen Methoden von Vekua. Dazu werden hyperkomplexe Verallgemeinerungen des komplexen Pi-Operators untersucht und auf die Lösung von hyperkomplexen Beltramigleichungen angewandt. / A modified Cauchy kernel is introduced over unbounded domains whose complement contain non-empty open sets. Basic results on Clifford analysis over bounded domains are now carried over to this more general context. In the end boundary value problems, e.g. for the Stokes-system or the Navier-Stokes-system, will be studied in the case of an unbounded domain without using weighted Sobolev spaces. In the latter part of this paper we deal with hypercomplex generalizations of the complex Pi-operator which turn out to have most of the useful properties of their complex origin. Afterwards the application of this operator to the solution of hypercomplex Beltrami equations will be studied.
6

Nonhomogeneous boundary value problem for the stationary Navier-Stokes system in domains with noncompact boundaries / Stacionari Navjė-Stokso sistema su nehomogenine kraštine sąlyga srityse su nekompaktiškais kraštais

Kaulakytė, Kristina 24 January 2013 (has links)
In the thesis there is studied nonhomogenous boundary value problem for the stationary Navier-Stokes system in domains which may have two types of outlets to infinity: paraboloidal and layer type. The boundary is multiply connected. It consists of connected noncompact components, forming the outer boundary, and connected compact components, forming the inner boundary. We suppose that the fluxes over the components of the inner boundary are sufficiently small, while we do not impose any restrictions on fluxes over the infinite components of the outer boundary. We prove that the formulated problem admits at least one weak solution which, depending on the geometry of the domain, may have either finite or infinite Dirichlet integral. / Disertacijoje nagrinėjama stacionari Navjė-Stokso sistema su nehomogenine kraštine sąlyga srityse su išėjimais į begalybę. Bendru atveju išėjimai į begalybę gali būti tiek paraboloidiniai, tiek sluoksnio tipo. Srities kraštą sudaro baigtinis skaičius nekompaktiškų jungių komponenčių, kurios suformuoja išorininį kraštą, ir baigtinis skaičius kompaktiškų jungių komponenčių, kurios suformuoja vidinį srities kraštą. Darydami prielaidą, kad srautai per vidinio krašto komponentes yra pakankamai maži, o srautų dydžiui per išorinio krašto komponentes nedarant jokių apribojimų, įrodome suformuluoto uždavinio bent vieno sprendinio egzistavimą. Priklausomai nuo srities geometrijos, uždavinio sprendinys gali turėti tiek baigtinį, tiek begalinį Dirichlė integralą.
7

Stacionari Navjė-Stokso sistema su nehomogenine kraštine sąlyga srityse su nekompaktiškais kraštais / Nonhomogeneous boundary value problem for the stationary Navier-Stokes system in domains with noncompact boundaries

Kaulakytė, Kristina 24 January 2013 (has links)
Disertacijoje nagrinėjama stacionari Navjė-Stokso sistema su nehomogenine kraštine sąlyga srityse su išėjimais į begalybę. Bendru atveju išėjimai į begalybę gali būti tiek paraboloidiniai, tiek sluoksnio tipo. Srities kraštą sudaro baigtinis skaičius nekompaktiškų jungių komponenčių, kurios suformuoja išorininį kraštą, ir baigtinis skaičius kompaktiškų jungių komponenčių, kurios suformuoja vidinį srities kraštą. Darydami prielaidą, kad srautai per vidinio krašto komponentes yra pakankamai maži, o srautų dydžiui per išorinio krašto komponentes nedarant jokių apribojimų, įrodome suformuluoto uždavinio bent vieno sprendinio egzistavimą. Priklausomai nuo srities geometrijos, uždavinio sprendinys gali turėti tiek baigtinį, tiek begalinį Dirichlė integralą. / In the thesis there is studied nonhomogenous boundary value problem for the stationary Navier-Stokes system in domains which may have two types of outlets to infinity: paraboloidal and layer type. The boundary is multiply connected. It consists of connected noncompact components, forming the outer boundary, and connected compact components, forming the inner boundary. We suppose that the fluxes over the components of the inner boundary are sufficiently small, while we do not impose any restrictions on fluxes over the infinite components of the outer boundary. We prove that the formulated problem admits at least one weak solution which, depending on the geometry of the domain, may have either finite or infinite Dirichlet integral.
8

Soluções particulares para as equações de Navier-Stokes tridimensionais transientes

Beck, Daniel January 2009 (has links)
Este Trabalho apresenta novas soluções exatas para as equações de Navier – Stokes transientes tridimensionais para escoamentos viscosos incompressíveis. Estas soluções são obtidas por meio de Split e Transformações Auto-Bäcklund. O procedimento de Split desacopla as equações de Navier – Stokes em dois sistemas de equações diferenciais parciais, um linear e outro não-linear, ambos não-homogêneos. O sistema linear, que contém somente termos viscosos e derivadas temporais, é resolvido via Transformações Auto-Bäcklund induzidas por relações de comutação, fornecendo o campo de velocidades. Os componentes do vetor velocidade são então substituídos no sistema não-linear a fim de obter o correspondente campo de pressões. A resolução do sistema não-linear para a pressão pode ser obtida tanto numericamente (via integração direta) quanto analiticamente, empregando a equação de Helmholtz. O objetivo do presente trabalho é encontrar expressões analíticas para o campo de velocidades e obter resultados numéricos para o campo de pressão associado. O caráter híbrido das soluções proporciona uma redução significativa do tempo de processamento requerido para a simulação de escoamentos viscosos, o qual praticamente se reduz ao tempo demandado para a tarefa de pós-processamento. Com esse objetivo em mente, foi desenvolvida uma formulação tridimensional escalar para a função corrente, a fim de reduzir o tempo requerido na tarefa mais dispendiosa de pós-processamento, a saber, o traçado das linhas de corrente em torno de corpos submersos de formato arbitrário. Neste estágio de desenvolvimento, esta formulação é empregada para produzir mapas de linhas de corrente para escoamentos viscosos em torno de uma esfera para números de Reynolds elevados. / This work presents new exact solutions to the unsteady three dimensional Navier-Stokes equations for incompressible viscous flows. These solutions are obtained by means of split and auto-Bäcklund transformations. The splitting procedure decouples the Navier-Stokes equations into a linear and a nonlinear inhomogeneous system of partial differential equations. The linear system, which contains only viscous terms and time derivatives, is solved via auto-Bäcklund transformations induced by commutation relations, furnishing the velocity field. The components of the velocity vector are then replaced into the nonlinear system to obtain the corresponding pressure field. The solution of the nonlinear system for the pressure variable can be carried out either numerically (by direct integration) or analytically, using the Helmholtz equation . The aim of the proposed work is to find analytical expressions for the velocity field and to obtain numerical results to the associated pressure field. The hybrid character of the solutions provides a significant reduction on the time processing required to simulate viscous flows, which virtually reduces to the time demanded to execute post-processing tasks. Taking this fact in mind, a three dimensional scalar formulation for the streamfunction was developed in order to simplify the most time-consuming post-processing task required, e.g., plotting the streamlines around arbitrary shaped bodies. At this stage of development, this formulation is employed to produce streamline maps for viscous flows around a sphere for high Reynolds numbers.
9

Soluções particulares para as equações de Navier-Stokes tridimensionais transientes

Beck, Daniel January 2009 (has links)
Este Trabalho apresenta novas soluções exatas para as equações de Navier – Stokes transientes tridimensionais para escoamentos viscosos incompressíveis. Estas soluções são obtidas por meio de Split e Transformações Auto-Bäcklund. O procedimento de Split desacopla as equações de Navier – Stokes em dois sistemas de equações diferenciais parciais, um linear e outro não-linear, ambos não-homogêneos. O sistema linear, que contém somente termos viscosos e derivadas temporais, é resolvido via Transformações Auto-Bäcklund induzidas por relações de comutação, fornecendo o campo de velocidades. Os componentes do vetor velocidade são então substituídos no sistema não-linear a fim de obter o correspondente campo de pressões. A resolução do sistema não-linear para a pressão pode ser obtida tanto numericamente (via integração direta) quanto analiticamente, empregando a equação de Helmholtz. O objetivo do presente trabalho é encontrar expressões analíticas para o campo de velocidades e obter resultados numéricos para o campo de pressão associado. O caráter híbrido das soluções proporciona uma redução significativa do tempo de processamento requerido para a simulação de escoamentos viscosos, o qual praticamente se reduz ao tempo demandado para a tarefa de pós-processamento. Com esse objetivo em mente, foi desenvolvida uma formulação tridimensional escalar para a função corrente, a fim de reduzir o tempo requerido na tarefa mais dispendiosa de pós-processamento, a saber, o traçado das linhas de corrente em torno de corpos submersos de formato arbitrário. Neste estágio de desenvolvimento, esta formulação é empregada para produzir mapas de linhas de corrente para escoamentos viscosos em torno de uma esfera para números de Reynolds elevados. / This work presents new exact solutions to the unsteady three dimensional Navier-Stokes equations for incompressible viscous flows. These solutions are obtained by means of split and auto-Bäcklund transformations. The splitting procedure decouples the Navier-Stokes equations into a linear and a nonlinear inhomogeneous system of partial differential equations. The linear system, which contains only viscous terms and time derivatives, is solved via auto-Bäcklund transformations induced by commutation relations, furnishing the velocity field. The components of the velocity vector are then replaced into the nonlinear system to obtain the corresponding pressure field. The solution of the nonlinear system for the pressure variable can be carried out either numerically (by direct integration) or analytically, using the Helmholtz equation . The aim of the proposed work is to find analytical expressions for the velocity field and to obtain numerical results to the associated pressure field. The hybrid character of the solutions provides a significant reduction on the time processing required to simulate viscous flows, which virtually reduces to the time demanded to execute post-processing tasks. Taking this fact in mind, a three dimensional scalar formulation for the streamfunction was developed in order to simplify the most time-consuming post-processing task required, e.g., plotting the streamlines around arbitrary shaped bodies. At this stage of development, this formulation is employed to produce streamline maps for viscous flows around a sphere for high Reynolds numbers.
10

Resultados teÃricos de controlabilidade para algumas EDPs nÃo-lineares da fÃsica / Theoretical controllability results for some nonlinear PDEs from physics

Ivaldo Tributino de Sousa 07 December 2015 (has links)
CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Esta tese trata do controle nulo local de um problema de fronteira-livre para a equaÃÃo do calor semilinear 1D com controles distribuÃdos (apoiado localmente no espaÃo) ou controles de fronteira (atuando em x = 0). provamos que, se o tempo final T à fixado e o estado inicial à suficientemente pequeno, existe controles que dirigem o estado exatamente para descansar no tempo t = T. AlÃm disso, analisamos a controlabilidade nulo de um sistema nÃo-linear 1D que modela a interaÃÃo de um fluido e sua fronteira. O fluido à governado pela equaÃÃo de Burgers viscosa e os controles distribuÃdos. Por Ãltimo, vamos lidar com o sistema de Navier-Stokes e Boussinesq 3D, definido em um cubo. Neste contexto, provamos um resultado sobre a sua controlabilidade aproximada global por meio de controles de fronteira que atuam em alguma parte da faces do cubo. / This Thesis deals with the local null control of a free-boundary problem for the 1D semilinear heat equation with distributed controls (locally supported in space) or boundary controls (acting at x = 0). we prove that, if the final time T is fixed and the initial state is sufficiently small, there exists controls that drive the state exactly to rest at time t = T. Furthermore, we analyze the null controllability of a 1D nonlinear system which models the interaction of a fluid and its boundary. The fluid is governed by the viscous Burgers equation and the distributed controls. Lastly, we deal with the 3D Navier-Stokes and Boussinesq system, posed in a cube. In this context, we prove a result concerning its global approximate controllability by means of boundary controls which act in some part of cube faces.

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