Дисертації з теми "Reaction-convection-diffusion equations"
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Sun, Xiaodi. "Metastable dynamics of convection-diffusion-reaction equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/NQ34630.pdf.
Повний текст джерелаSeymen, Zahire. "Solving Optimal Control Time-dependent Diffusion-convection-reaction Equations By Space Time Discretizations." Phd thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615399/index.pdf.
Повний текст джерелаHernandez, Velazquez Hector Alonso. "Numerical stabilization for multidimensional coupled convection-diffusion-reaction equations: Applications to continuum dislocation transport." Doctoral thesis, Universite Libre de Bruxelles, 2017. https://dipot.ulb.ac.be/dspace/bitstream/2013/257833/6/contratHH.pdf.
Повний текст джерелаDoctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
Ahmed, Naveed, and Gunar Matthies. "Higher order continuous Galerkin−Petrov time stepping schemes for transient convection-diffusion-reaction equations." Cambridge University Press, 2015. https://tud.qucosa.de/id/qucosa%3A39044.
Повний текст джерелаMbroh, Nana Adjoah. "On the method of lines for singularly perturbed partial differential equations." University of the Western Cape, 2017. http://hdl.handle.net/11394/5679.
Повний текст джерелаMany chemical and physical problems are mathematically described by partial differential equations (PDEs). These PDEs are often highly nonlinear and therefore have no closed form solutions. Thus, it is necessary to recourse to numerical approaches to determine suitable approximations to the solution of such equations. For solutions possessing sharp spatial transitions (such as boundary or interior layers), standard numerical methods have shown limitations as they fail to capture large gradients. The method of lines (MOL) is one of the numerical methods used to solve PDEs. It proceeds by the discretization of all but one dimension leading to systems of ordinary di erential equations. In the case of time-dependent PDEs, the MOL consists of discretizing the spatial derivatives only leaving the time variable continuous. The process results in a system to which a numerical method for initial value problems can be applied. In this project we consider various types of singularly perturbed time-dependent PDEs. For each type, using the MOL, the spatial dimensions will be discretized in many different ways following fitted numerical approaches. Each discretisation will be analysed for stability and convergence. Extensive experiments will be conducted to confirm the analyses.
Ahmed, Naveed [Verfasser], and Lutz [Akademischer Betreuer] Tobiska. "Stabilized finite element methods applied to transient convection-diffusion-reaction and population balance equations / Naveed Ahmed. Betreuer: Lutz Tobiska." Magdeburg : Universitätsbibliothek, 2011. http://d-nb.info/1047559021/34.
Повний текст джерелаSimon, Kristin [Verfasser]. "Higher order stabilized surface finite element methods for diffusion-convection-reaction equations on surfaces with and without boundary / Kristin Simon." Magdeburg : Universitätsbibliothek, 2017. http://d-nb.info/1147834520/34.
Повний текст джерелаLao, Kun Leng. "Multigrid algorithm based on cyclic reduction for convection diffusion equations." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148274.
Повний текст джерелаNadukandi, Prashanth. "Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems." Doctoral thesis, Universitat Politècnica de Catalunya, 2011. http://hdl.handle.net/10803/109155.
Повний текст джерелаPresentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de Stokes, respectivamente. El trabajo comienza con un analisis a priori de un metodo de recuperaci6n de la consistencia de algunos metodos de estabilizaci6n que pertenecen al marco de Petrov-Galerkin. Hallamos que el uso de algunas de las practicas estandar (por ejemplo, la eoria de Matriz-M) para el diserio de metodos numericos esencialmente no oscilatorios no es apropiado cuando utilizamos los metodos de recu eraci6n de la consistencia. Por 10 tanto, con res ecto a la estabilizaci6n de conveccion, no preferimos tales metodos de recuperacion . A continuacion, presentamos el diser'io de un metodo de Petrov-Galerkin de alta-resolucion (HRPG) para el problema CDR. La estructura del metodo en 10 es identico al metodo CAU [doi: 10.1016/0045-7825(88)90108-9] excepto en la definicion de los parametros de estabilizacion. Esta estructura tambien se puede obtener a traves de la formulacion del calculo finito (FIC) [doi: 10.1 016/S0045- 7825(97)00119-9] usando una definicion adecuada de la longitud caracteristica. El prefijo de "alta-resolucion" se utiliza aqui en el sentido popularizado por Harten, es decir, tener una solucion con una precision de segundo orden en los regimenes suaves y ser esencialmente no oscilatoria en los regimenes no regulares. El diser'io en 10 se embarca en el problema de eludir el fenomeno de Gibbs observado en las proyecciones de tipo L2. A continuacion, estudiamos las condiciones de los parametros de estabilizacion para evitar las oscilaciones globales debido al ermino convectivo. Combinamos los dos resultados (una conjetura) para tratar el problema COR, cuya solucion numerica sufre de oscilaciones numericas del tipo global, Gibbs y dispersiva. Tambien presentamos una extension multidimensional del metodo HRPG utilizando los elementos finitos multi-lineales. fa. continuacion, proponemos un esquema compacto de orden superior (que incluye dos parametros) en mallas estructuradas para la ecuacion de Helmholtz. Haciendo igual ambos parametros, se recupera la interpolacion lineal del metodo de elementos finitos (FEM) de tipo Galerkin y el clasico metodo de diferencias finitas centradas. En 10 este esquema es identico al metodo AIM [doi: 10.1 016/0771 -050X(82)90002-X] y en 20 eligiendo el valor de 0,5 para ambos parametros, se recupera el esquema compacto de cuarto orden de Pade generalizada en [doi: 10.1 006/jcph.1 995.1134, doi: 10.1 016/S0045-7825(98)00023-1] (con el parametro V = 2). Seguimos [doi: 10.1 016/0045-7825(95)00890-X] para el analisis de este esquema y comparamos su rendimiento en las mallas uniformes con el de "FEM cuasi-estabilizado" (QSFEM) [doi: 10.1016/0045-7825 (95) 00890-X]. Presentamos expresiones genericas de los para metros que garantiza una precision dispersiva de sexto orden si ambos parametros son distintos y de cuarto orden en caso de ser iguales. En este ultimo caso, presentamos la expresion del parametro que minimiza el error maxima de fase relativa en 20. Tambien proponemos una formulacion de tipo Petrov-Galerkin ~ue recupera los esquemas antes mencionados en mallas estructuradas. Presentamos estudios de convergencia del error en la norma de tipo L2, la semi-norma de tipo H1 y la norma Euclidiana tipo I~ y mostramos que la perdida de estabilidad del operador de Helmholtz ("pollution effect") es incluso pequer'ia para grandes numeros de onda. Por ultimo, presentamos una coleccion de metodos FE estabilizado para el problema de Stokes desarrollados a raves del metodo FIC de primer orden y de segundo orden. Mostramos que varios metodos FE de estabilizacion existentes y conocidos como el metodo de penalizacion, el metodo de Galerkin de minimos cuadrados (GLS) [doi: 10.1016/0045-7825(86)90025-3], el metodo PGP (estabilizado a traves de la proyeccion del gradiente de presion) [doi: 10.1 016/S0045-7825(96)01154-1] Y el metodo OSS (estabilizado a traves de las sub-escalas ortogonales) [doi: 10.1016/S0045-7825(00)00254-1] se recuperan del marco general de FIC. Oesarrollamos una nueva familia de metodos FE, en adelante denominado como PLS (estabilizado a traves del Laplaciano de presion) con las formas no lineales y consistentes de los parametros de estabilizacion. Una caracteristica distintiva de la familia de los metodos PLS es que son no lineales y basados en el residuo, es decir, los terminos de estabilizacion dependera de los residuos discretos del momento y/o las ecuaciones de incompresibilidad. Oiscutimos las ventajas y desventajas de estas tecnicas de estabilizaci6n y presentamos varios ejemplos de aplicacion
Galbally, David. "Nonlinear model reduction for uncertainty quantification in large-scale inverse problems : application to nonlinear convection-diffusion-reaction equation." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43079.
Повний текст джерелаIncludes bibliographical references (p. 147-152).
There are multiple instances in science and engineering where quantities of interest are evaluated by solving one or several nonlinear partial differential equations (PDEs) that are parametrized in terms of a set of inputs. Even though well-established numerical techniques exist for solving these problems, their computational cost often precludes their use in cases where the outputs of interest must be evaluated repeatedly for different values of the input parameters such as probabilistic analysis applications. In this thesis we present a model reduction methodology that combines efficient representation of the nonlinearities in the governing PDE with an efficient model-constrained, greedy algorithm for sampling the input parameter space. The nonlinearities in the PDE are represented using a coefficient-function approximation that enables the development of an efficient offline-online computational procedure where the online computational cost is independent of the size of the original high-fidelity model. The input space sampling algorithm used for generating the reduced space basis adaptively improves the quality of the reduced order approximation by solving a PDE-constrained continuous optimization problem that targets the output error between the reduced and full order models in order to determine the optimal sampling point at every greedy cycle. The resulting model reduction methodology is applied to a highly nonlinear combustion problem governed by a convection-diffusion-reaction PDE with up to 3 input parameters. The reduced basis approximation developed for this problem is up to 50, 000 times faster to solve than the original high-fidelity finite element model with an average relative error in prediction of outputs of interest of 2.5 - 10-6 over the input parameter space. The reduced order model developed in this thesis is used in a novel probabilistic methodology for solving inverse problems.
(cont) The extreme computational cost of the Bayesian framework approach for inferring the values of the inputs that generated a given set of empirically measured outputs often precludes its use in practical applications. In this thesis we show that using a reduced order model for running the Markov
by David Galbally.
S.M.
Farrell, Troy W. "The mathematical modelling of primary alkaline battery cathodes." Thesis, Queensland University of Technology, 1998.
Знайти повний текст джерелаAkman, Tugba. "Discontinuous Galerkin Methods For Time-dependent Convection Dominated Optimal Control Problems." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613394/index.pdf.
Повний текст джерелаDeolmi, Giulia. "Computational Parabolic Inverse Problems." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3423351.
Повний текст джерелаIn questa tesi viene presentato un approccio numerico volto alla risoluzione di problemi inversi parabolici, basato sull'utilizzo di una parametrizzazione adattativa. L'algoritmo risolutivo viene descritto per due specici problemi: mentre il primo consiste nella stima della corrosione di una faccia incognita del dominio, il secondo ha come scopo la quanticazione di inquinante immesso in un fiume.
Godongwana, Buntu. "Effect of nutrient momentum and mass transport on membrane gradostat reactor efficiency." Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2149.
Повний текст джерелаSince the first uses of hollow-fiber membrane bioreactors (MBR’s) to immobilize whole cells were reported in the early 1970’s, this technology has been used in as wide ranging applications as enzyme production to bone tissue engineering. The potential of these devices in industrial applications is often diminished by the large diffusional resistances of the membranes. Currently, there are no analytical studies on the performance of the MBR which account for both convective and diffusive transport. The purpose of this study was to quantify the efficiency of a biocatalytic membrane reactor used for the production of enzymes. This was done by developing exact solutions of the concentration and velocity profiles in the different regions of the membrane bioreactor (MBR). The emphasis of this study was on the influence of radial convective flows, which have generally been neglected in previous analytical studies. The efficiency of the MBR was measured by means of the effectiveness factor. An analytical model for substrate concentration profiles in the lumen of the MBR was developed. The model was based on the solution of the Navier-Stokes equations and Darcy’s law for velocity profiles, and the convective-diffusion equation for the solute concentration profiles. The model allowed for the evaluation of the influence of both hydrodynamic and mass transfer operating parameters on the performance of the MBR. These parameters include the fraction retentate, the transmembrane pressure, the membrane hydraulic permeability, the Reynolds number, the axial and radial Peclet numbers, and the dimensions of the MBR. The significant findings on the hydrodynamic studies were on the influence of the fraction retentate. In the dead-end mode it was found that there was increased radial convective flow, and hence more solute contact with the enzymes/biofilm immobilised on the surface of the membrane. The improved solute-biofilm contact however was only limited to the entrance half of the MBR. In the closed shell mode there was uniform distribution of solute, however, radial convective flows were significantly reduced. The developed model therefore allowed for the evaluation of an optimum fraction retentate value, where both the distribution of solutes and radial convective flows could be maximised.
Brenner, Konstantin. "Méthodes de volumes finis sur maillages quelconques pour des systèmes d'évolution non linéaires." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00647336.
Повний текст джерелаLin, Shin-Hong, and 林信宏. "Equilibrium Models to the Reaction-Convection-Diffusion Equations in Hydrogeology." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/3hw3we.
Повний текст джерела國立中央大學
數學研究所
96
In this thesis we introduce the equilibrium model of hydrogeology. We give the notations and assumptions in hydrogeology and introduce the adsorption kinetics. The positive solutions of the model is studied by the maximum principle, and energy method is provided to get the stability of small perturbations. Moreover, the existence and behavior of traveling wave solutions to equilibrium model is considered. Finally, we study the discontinuous traveling waves and gives two applications.
(5929550), Difeng Cai. "ROBUST AND EXPLICIT A POSTERIORI ERROR ESTIMATION TECHNIQUES IN ADAPTIVE FINITE ELEMENT METHOD." Thesis, 2019.
Знайти повний текст джерелаSrivastava, Shweta. "Stabilization Schemes for Convection Dominated Scalar Problems with Different Time Discretizations in Time dependent Domains." Thesis, 2017. http://etd.iisc.ernet.in/2005/3574.
Повний текст джерелаDomingues, Luís Évora. "Drug delivery assisted by ultrasound in viscoelastic materials." Master's thesis, 2022. http://hdl.handle.net/10316/99380.
Повний текст джерелаThe main goal of this work is the analytical and numerical study of a differential system defined by an integro-differential equation of hyperbolic type and a convection-diffusion-reaction equation. This system arises in the mathematical modeling of drug delivery enhanced by ultrasound. In this case, the hyperbolic equation describes the target displacement generated by ultrasound and the second equation describes the drug transport. The parabolic equation depends on the displacement and eventually on its time derivative. The differential system is completed by initial conditions and homogeneous boundary conditions of Dirichlet type. We establish existence, uniqueness and stability results for the displacement and concentration in both the continuous and the semi-discrete cases. In the continuous case, the existence result for the displacement problem is established considering the method of separation of variables, the stability is proved considering the energy method that allows us to get an estimate for the potential and kinetic energies. The existence of concentration is obtained applying a known result. The stability is proved using again the energy method. In the stability analysis of the semi-discrete approximations for the displacement and concentration, we follow discrete versions of the arguments used in the continuous case. The convergence analysis of the semi-discrete approximations is also based in the discrete energy method and second convergence order is obtained. We observe that the spatial truncation error is only of first order with respect to the infinity norm. The numerical results illustrating the theoretical results established are also included.
O objectivo principal deste trabalho é o estudo analítico e numérico de um sistema diferencial definido por uma equação integro-diferencial do tipo hiperbólico e uma equação de convecção-difusão-reação. Este sistema surge na modelação matemática da administração de fármacos assistida por ultrassom. Neste caso, a equação hiperbólica descreve o deslocamento no meio gerado pelo ultrassom e a segunda equação descreve o transporte do fármaco. A equação parabólica depende do deslocamento e eventualmente da sua derivada temporal. O sistema diferencial é completado com condições iniciais e condições de fronteira homogéneas de Dirichlet. Estabelecemos resultados de existência, unicidade e estabilidade para o deslocamento e para a concentração tanto no caso contínuo como no caso semi-discreto. No caso contínuo, o resultado da existência para o problema do deslocamento é estabelecido considerando o método de separação de variáveis, a estabilidade é provada considerando o método da energia que nos permite encontrar uma estimativa para as energias potencial e cinética. A existência da concentração é obtida aplicando um resultado conhecido. A estabilidade é provada usando novamente o método da energia. Na análise da estabilidade da aproximação semi-discreta para o deslocamento, seguimos versões discretas dos argumentos usados no caso contínuo. A análise da convergência das aproximações semi-discretas é também baseada no método da energia discreto e é obtida segunda ordem de convergência. Observamos que o erro de truncatura espacial é apenas de primeira ordem em relação à norma infinito. Os resultados numéricos ilustrando os resultados teóricos obtidos são também incluídos neste trabalho.