Готові списки джерел за темами / Hele-Shaw problem

Добірка наукової літератури з теми "Hele-Shaw problem"

Автор: Grafiati

Опубліковано: 6 липня 2024

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Статті в журналах з теми "Hele-Shaw problem":

CROWDY, DARREN G. "Hele-Shaw flows and water waves." Journal of Fluid Mechanics 409 (April 25, 2000): 223–42. http://dx.doi.org/10.1017/s0022112099007685.

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By adapting a new mathematical approach to the problem of steady free-surface Euler flows with surface tension recently devised by the present author, it is demonstrated that exact solutions for steady, free-surface multipole-driven Hele-Shaw flows with surface tension can be constructed using similar methods. Moreover, a (one-way) mathematical transformation between exact solutions to the two distinct free-boundary problems is identified: known exact solutions for free-surface Euler flows with surface tension are shown to automatically generate steady quadrupolar-driven Hele-Shaw flows (with non-zero surface tension) existing in exactly the same domain with the same free surface. This correspondence highlights the essential dynamical differences between the two physical problems. Using the transformation, the exact Hele-Shaw analogues of all known exact solutions for free-surface Euler flows (including Crapper's classic capillary water wave solution) are catalogued thereby producing many previously unknown exact solutions for steady Hele-Shaw flows with capillarity. In particular, this paper reports what are believed to be the first known exact solutions for Hele-Shaw flows with surface tension in a doubly-connected fluid region.

Kimura, Masato, Daisuke Tagami, and Shigetoshi Yazaki. "Polygonal Hele–Shaw problem with surface tension." Interfaces and Free Boundaries 15, no. 1 (2013): 77–93. http://dx.doi.org/10.4171/ifb/295.

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Vasil’ev †, Alexander. "Robin's Modulus in a Hele-Shaw Problem." Complex Variables, Theory and Application: An International Journal 49, no. 7-9 (June 10, 2004): 663–72. http://dx.doi.org/10.1080/02781070410001732188.

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Mellet, Antoine, Benoît Perthame, and Fernando Quirós. "A Hele–Shaw problem for tumor growth." Journal of Functional Analysis 273, no. 10 (November 2017): 3061–93. http://dx.doi.org/10.1016/j.jfa.2017.08.009.

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Yadav, Dhananjay. "The effect of pulsating throughflow on the onset of magneto convection in a layer of nanofluid confined within a Hele-Shaw cell." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 233, no. 5 (March 13, 2019): 1074–85. http://dx.doi.org/10.1177/0954408919836362.

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In this article, the joint effect of pulsating throughflow and magnetic field on the onset of convective instability in a nanofluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory and frozen profile approach. The model utilized for nanofluid combines the impacts of Brownian motion and thermophoresis, while for Hele-Shaw cell, Hele-Shaw model is considered. The Galerkin technique is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability framework is examined analytically. It is observed that the pulsating throughflow and magnetic field have both stabilizing effects. The impact of increasing the Hele-Shaw number [Formula: see text], the modified diffusive ratio [Formula: see text] and the nanoparticle Rayleigh number [Formula: see text] is to quicken the convective motion, while the Lewis number [Formula: see text] has dual impact on the stability framework in the existence of pulsating throughflow. It is also established that the oscillatory mode of convective motion is possible only when the value of the magnetic Prandtl number [Formula: see text] is not greater than unity.

Saffman, P. G. "Viscous fingering in Hele-Shaw cells." Journal of Fluid Mechanics 173 (December 1986): 73–94. http://dx.doi.org/10.1017/s0022112086001088.

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The phenomenon of interfacial motion between two immiscible viscous fluids in the narrow gap between two parallel plates (Hele-Shaw cell) is considered. This flow is currently of interest because of its relation to pattern selection mechanisms and the formation of fractal, structures in a number of physical applications. Attention is concentrated on the fingers that result from the instability when a less-viscous fluid drives a more-viscous one. The status of the problem is reviewed and progress with the thirty-year-old problem of explaining the shape and stability of the fingers is described. The paradoxes and controversies are both mathematical and physical. Theoretical results on the structure and stability of steady shapes are presented for a particular formulation of the boundary conditions at the interface and compared with the experimental phenomenon. Alternative boundary conditions and future approaches are discussed.

Moog, Mathias, Rainer Keck, and Aivars Zemitis. "SOME NUMERICAL ASPECTS OF THE LEVEL SET METHOD." Mathematical Modelling and Analysis 3, no. 1 (December 15, 1998): 140–51. http://dx.doi.org/10.3846/13926292.1998.9637097.

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Many practical applications imply the solution of free boundary value problems. If the free boundary is complex and can change its topology, it will be hard to solve such problems numerically. In recent years a new method has been developed, which can handle boundaries with complex geometries. This new method is called the level set method. However, the level set method also has some drawbacks, which are mainly concerning conservation of mass or numerical instabilities of the boundaries. Our aim is to analyze some aspects of the level set method on the basis of two‐phase flow in a Hele‐Shaw cell. We investigate instabilities of two‐phase flow between two parallel plates. A solution of the linearized problem is obtained analytically in order to check whether the numerical schemes compute reasonable results. The developed numerical scheme is based on finite difference approximations and the level set method. The equations of two‐phase Hele‐Shaw flow are written in a modified formulation using the one‐dimensional Dirac delta‐function. Since the level set function is not smooth enough after re‐initialization, special attention during the computation of curvature is needed. We propose a method that can solve the problems for two‐phase Hele‐Shaw flow with changing topology. The numerical solution shows good agreement with the analytical solution of the linearized problem. We describe the method below and analyze the results.

Rogosin, Sergei, and Tatsyana Vaitekhovich. "Hele-Shaw Model for Melting/Freezing with Two Dendrits." Materials Science Forum 553 (August 2007): 143–51. http://dx.doi.org/10.4028/www.scientific.net/msf.553.143.

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Melting/freezing process with two dendrits (or freeze “pipes”) is modelled by the complex Hele-Shaw moving boundary value problem in a doubly connected domain. The later is equivalently reduced to a couple of problems, namely, to the linear Riemann-Hilbert boundary value problem in a doubly connected domain and to evolution problem, which can be written in a form of an abstract Cauchy-Kovalevsky problem. The later is studied on the base of Nirenberg-Nishida theorem, and for the former a generalization of the Schwarz Alternation Method is proposed. By using composition of these two approaches we get the local in time solvability of this couple of problems in appropriate Banach space setting.

Rogosin, S. "Real variable Hele-Shaw problem with kinetic undercooling." Lobachevskii Journal of Mathematics 38, no. 3 (May 2017): 510–19. http://dx.doi.org/10.1134/s1995080217030210.

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Jerison, David, and Inwon Kim. "The one-phase Hele-Shaw problem with singularities." Journal of Geometric Analysis 15, no. 4 (December 2005): 641–67. http://dx.doi.org/10.1007/bf02922248.

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Дисертації з теми "Hele-Shaw problem":

Dallaston, Michael C. "Mathematical models of bubble evolution in a Hele-Shaw Cell." Thesis, Queensland University of Technology, 2013. https://eprints.qut.edu.au/63701/1/Michael_Dallaston_Thesis.pdf.

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This thesis concerns the mathematical model of moving fluid interfaces in a Hele-Shaw cell: an experimental device in which fluid flow is studied by sandwiching the fluid between two closely separated plates. Analytic and numerical methods are developed to gain new insights into interfacial stability and bubble evolution, and the influence of different boundary effects is examined. In particular, the properties of the velocity-dependent kinetic undercooling boundary condition are analysed, with regard to the selection of only discrete possible shapes of travelling fingers of fluid, the formation of corners on the interface, and the interaction of kinetic undercooling with the better known effect of surface tension. Explicit solutions to the problem of an expanding or contracting ring of fluid are also developed.

Jackson, Michael. "Interfacial instability analysis of viscous flows in a Hele-Shaw channel." Thesis, Queensland University of Technology, 2021. https://eprints.qut.edu.au/212417/1/Michael_Jackson_Thesis.pdf.

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When a less viscous fluid displaces a more viscous fluid inside a quasi-two-dimensional channel, the interface separating the two fluids can become highly unstable and perturbed. By assuming that the more viscous fluid is finite in volume, this thesis uses analytical and computational methods to investigate the effect of two fluid interfaces. The results could have implication in fields such as oil extraction, geology, and advanced manufacturing.

David, Noemi. "Asymptotic analysis for a model of tumor growth: from a cell density model to a Hele-Shaw problem." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17066/.

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In questa tesi si presenta l'analisi asintotica di un modello di crescita tumorale, seguendo l'articolo The Hele–Shaw Asymptotics for Mechanical Models of Tumor Growth (2014) di Perthame B., Quiròs F. e Vàzquez J.L. Tramite l'analisi asintotica è possibile costruire una correlazione tra i due principali approcci utilizzati nella descrizione del fenomeno: modelli della densità cellulare e problemi a frontiera libera. I primi descrivono l'evoluzione della popolazione cellulare e la sua interazione con fattori esterni (ossigeno, glucosio, sostanze chimiche) attraverso sistemi di equazioni differenziali. I secondi descrivono il movimento del tumore attraverso modelli a frontiera libera, in quanto, nelle prime fasi del suo sviluppo, i contorni del tumore sono ben definiti. Nel modello illustrato in questa tesi, si assume che il movimento delle cellule sia guidato dalla legge di Darcy, la quale è solitamente usata per descrivere il flusso di un fluido in un mezzo poroso. Si considera quindi una PME (porous medium equation) che governa l'evoluzione della densità cellulare. Si dimostra che il limite della soluzione dell'equazione esiste e soddisfa un problema a frontiera libera del tipo Hele-Shaw. Si dimostra inoltre l'unicità di tale soluzione limite. I risultati analoghi vengono dimostrati anche per un sistema che comprende una seconda equazione di diffusione-reazione, la quale descrive l'evoluzione della concentrazione di generici nutrienti (solitamente ossigeno e glucosio).

Estacio, Kémelli Campanharo. ""Simulação do processo de moldagem por injeção 2D usando malhas não estruturadas"." Universidade de São Paulo, 2004. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-28072004-145944/.

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Moldagem por injeção é um dos mais importantes processos industriais para produção de produtos plásticos finos. Esse processo é dividido essencialmente em quatro estágios: plastificação, preenchimento, empacotamento e resfriamento. O escoamento de um fluido caracterizado por alta viscosidade em uma cavidade estreita é um problema tipicamente encontrado em processos de moldagem por injeção.Neste caso, o escoamento pode ser descrito por uma formulação conhecida como aproximação de Hele-Shaw. Tal formulação pode ser derivada das equações de conservação tridimensionais usando um número de suposições a respeito do polímero injetado e da geometria da cavidade do molde, juntamente com a integração e o acoplamento das equações da conservação da quantidade de movimento e da continuidade. Essa formulação, referindo às limitações da geometria do molde como sendo canais estreitos e quase sem curvatura, é comumente denominada formulação 2 1/2D. Neste trabalho, é apresentada uma técnica para a simulação da fase de preenchimento de um processo de moldagem por injeção, usando essa formulação 2 1/2D, com um método de volumes finitos e malhas não estruturadas. O modelo de Cross modificado com dependência da temperatura de Arrhenius é empregado para descrever a viscosidade do polímero fundido. O campo de distribuição de temperatura é tridimensional e é resolvido usando um esquema semi-Lagrangeano baseado em volumes finitos. As malhas não estruturadas utilizadas são geradas por triangulação de Delaunay e o método numérico implementado usa a estrutura de dados topológica SHE - Singular Handle Edge, que é capaz de lidar com condições de contorno e singularidades, aspectos comumente encontrados em simulações numéricas de escoamento de fluidos.
Injection molding is one of the most important industrial processes for the manufacturing of thin plastic products. This process can be divided into four stages: plastic melting, filling, packing and cooling phases. The flow of a fluid characterized by high viscosity in a narrow gap is a problem typically found in injection molding processes. In this case, the flow can be described by a formulation known as Hele-Shaw approach. Such formulation can be btained from the three-dimensional conservation equation using a number of assumptions regarding the injected polymer and the geometry of the mold, together with the integration and the coupling of the momentum and continuity equations. This approach, referring to limitations of the mould geometry to narrow, weakly curved channels, is usually called 2 1/2D approach. In this work a technique for the simulation of the filling stage of the injection molding process, using this 2 1/2D approach, with a finite volume method and unstructured meshes, is presented. The modified-Cross model with Arrhenius temperature dependence is employed to describe the viscosity of the melt. The temperature field is 3D and it is solved using a semi-Lagrangian scheme based on the finite volume method. The employed unstructured meshes are generated by Delaunay triangulation and the implemented numerical method uses the topological data structure SHE - Singular Handle Edge, capable to deal with boundary conditions and singularities, aspects commonly found in numerical simulation of fluid flow.

Morrow, Liam Christopher. "A numerical investigation of Darcy-type moving boundary problems." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/204264/1/Liam_Morrow_Thesis.pdf.

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We investigate the development of interfacial instabilities and singularities that occur in solutions to Darcy-type moving boundary problems. We present a robust numerical scheme which can easily be adapted to a wide range of problems that, to date, have not yet been solved. Using this scheme, we provide insight into how perturbing the geometry of a Hele-Shaw cell can be used to control the development of interfacial patterns. Further, we consider how different physical effects influence the development of a singularity due to an air bubble contracting to a point or breaking up into multiple bubbles.

David, Noemi. "Incompressible limit and well-posedness of PDE models of tissue growth." Electronic Thesis or Diss., Sorbonne université, 2022. https://accesdistant.sorbonne-universite.fr/login?url=https://theses-intra.sorbonne-universite.fr/2022SORUS235.pdf.

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Les modèles de milieux poreux, en régime compressible ou incompressible, sont utilisés dans la littérature pour décrire les propriétés mécaniques des tissus vivants et en particulier de la croissance tumorale. Il est possible de construire un lien entre ces deux différentes représentations en utilisant une loi de pression raide. Dans la limite incompressible, les modèles compressibles conduisent à des problèmes de frontières libres de type Hele-Shaw. Nos travaux visent à étudier la limite de pression raide des équations de type milieu poreux motivées par le développement tumoral. Notre première étude concerne l’analyse et la simulation numérique d’un modèle incluant l’effet des nutriments. Ensuite, un système d’équations, dont le couplage est délicat, décrit la densité cellulaire et la concentration en nutriments. Pour cette raison, la dérivation de l’équation de pression dans la limite incompressible était un problème ouvert qui nécessite la compacité forte du gradient de pression. Pour l’établir, nous utilisons deux nouvelles idées : une version L3 de la célèbre estimation d’Aronson-Bénilan, également utilisée récemment pour des problèmes connexes, et une estimation L4 sur le gradient de pression (où l’exposant 4 est optimal). Nous étudions en outre l’optimalité de cette estimation par un schéma numérique upwind aux différences finies, que nous montrons être stable et asymptotic preserving. Notre deuxième étude est centrée sur l’équation de milieux poreux avec effets convectifs. Nous étendons les techniques développées pour le cas avec nutriments, trouvant ainsi la relation de complémentarité sur la pression limite. De plus, nous fournissons une estimation du taux de convergence à la limite incompressible. Enfin, nous étudions un système multi-espèces. En particulier, en tenant compte de l’hétérogénéité phénotypique, nous incluons une variable structurée dans le problème. Par conséquent, un système de diffusion croisée et dégénérée décrit l’évolution des distributions phénotypiques. En adaptant des méthodes récemment développées pour des systèmes à deux équations, nous prouvons l’existence de solutions faibles et nous passons à la limite incompressible. En outre, nous prouvons de nouveaux résultats de régularité sur la pression totale, qui est liée à la densité totale par une loi de puissance
Both compressible and incompressible porous medium models have been used in the literature to describe the mechanical aspects of living tissues, and in particular of tumor growth. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems of Hele-Shaw type where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. Then, a coupled system of equations describes the cell density and the nutrient concentration. For this reason, the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, also recently applied to related problems, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state

Huntingford, C. "Unstable Hele-Shaw and Stefan problems." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305462.

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Khalid, A. H. "Free boundary problems in a Hele-Shaw cell." Thesis, University College London (University of London), 2015. http://discovery.ucl.ac.uk/1463159/.

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The motion of a free boundary separating two immiscible fluids in an unbounded Hele-Shaw cell is considered. In the one-phase problem, a viscous fluid is separated from an inviscid fluid by a simple closed boundary. Preliminaries for a complex variable technique are presented by which the one-phase problem can be solved explicitly via conformal mappings. The Schwarz function of the boundary plays a major role giving rise to the so called Schwarz function equation which governs the evolution of exact solutions. The Schwarz function approach is used to study the stability of a translating elliptical bubble due to a uniform background flow, and the stability of a blob (or bubble) subject to an external electric field. The one-phase problem of a translating free boundary and of a free boundary subject to an external field are studied numerically. A boundary integral method is formulated in the complex plane by considering the Cauchy integral formula and the complex velocity of a fluid particle on the free boundary. In the case of a free boundary subject to an external electric field due to a point charge, it is demonstrated that a stable steady state is achieved for appropriate charge strength. The method is also employed to study breakup of a single translating bubble in which the Schwarz function singularities (shown to be stationary) of the initial boundary play an important role. The two-phase problem is also considered, where the free boundary now separates two viscous fluids, and the construction of exact solutions is studied. The one-phase numerical model is enhanced, where a boundary integral method is formulated to accommodate the variable pressure in both viscous phases. Some numerical experiments are presented with a comparison to analytical results, in particular for the case where the free boundary is driven by a uniform background flow.

Mostefai, Mohamed Sadek. "Déduction rigoureuse de l'équation de Reynolds à partir d'un système modélisant l'écoulement à faible épaisseur d'un fluide micropolaire, et étude de deux problèmes à frontière libre : Hele-Shaw généralisé et Stephan à deux phases pour un fluide non newtonien." Saint-Etienne, 1997. http://www.theses.fr/1997STET4019.

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Dans le chapitre 1, on considère le modèle micropolaire de Navier-Stokes avec conditions de bords de type Dirichlet non homogènes en dimension deux. On donnera un résultat d'existence d'une solution faible en utilisant le théorème du point fixe de Leray-Schauder, puis on prouvera l'unicité de la solution faible du problème sous certaines hypothèses. On établiera une justification mathématique de l’équation de Reynolds généralisé à partir de ce modèle là. On étudiera ensuite la forme de l'équation de Reynolds suivant le choix de la viscosité et des données initiales. Dans le chapitre 2, nous considérons le modèle de Hele-Shaw généralisé dans une cellule laminaire, qui consiste à injecter du fluide, avec un débit non constant w 0, à travers un trou de frontière 1, situé sur l'une des deux surfaces ; et à tenir compte que l'une des surfaces a une géométrie quelconque et animée d'un mouvement relatif vertical. En introduisant un changement de variable de type Baiocchi, le problème initial se ramène à l'étude d'une inéquation variationnelle avec terme de Volterra. L'existence d'une solution pour cette dernière est donnée par le théorème du point fixe de Banach. Des résultats de régularité en espace pour la solution seront prouvés en introduisant un problème pénalisé et en utilisant la méthode de Rothe (semi-discrétisation en temps), puis on montrera que la dérivée par rapport à t de la solution de l'inéquation variationnelle est dans l#(0, t, h#2()), ce dernier résultat nous permet de revenir au problème initial. Dans le chapitre 3, on considère un problème de Stefan à deux phases avec convection. Le problème est gouverné par un système couple non linéaire, comprenant la loi de Darcy pour un fluide non newtonien et l'équation d'équilibre d'énergie avec second membre dans l#1. Pour prouver l'existence de solutions du problème faible on introduira une famille de solutions approchées (#, p#), > 0, définies sur le domaine entier , en insérant une fonction de pénalité convenable dans l'équation de pression. On considère ensuite séparement les problèmes en # et p#, respectivement, et en utilisant le principe de point fixe de Schauder, on montre l'existence de couples solutions (#, p#) du problème approché, pour tout > 0. En faisant tendre vers zéro, on montre que les solutions du problème approché convergent vers une limite (, p) qui est une solution faible du problème variationnel. On montre aussi que la fonction est continue d'où le domaine où > 0 est un ensemble ouvert, et l'interface des deux phases est définie a posteriori comme l'ensemble de niveau = 0. On établira, enfin, quelques relations entre les solutions faibles et classiques, dans le cas d’une courbe assez régulière

Jonsson, Karl. "Two Problems in non-linear PDE’s with Phase Transitions." Licentiate thesis, KTH, Matematik (Avd.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-223562.

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This thesis is in the field of non-linear partial differential equations (PDE), focusing on problems which show some type of phase-transition. A single phase Hele-Shaw flow models a Newtoninan fluid which is being injected in the space between two narrowly separated parallel planes. The time evolution of the space that the fluid occupies can be modelled by a semi-linear PDE. This is a problem within the field of free boundary problems. In the multi-phase problem we consider the time-evolution of a system of phases which interact according to the principle that the joint boundary which emerges when two phases meet is fixed for all future times. The problem is handled by introducing a parameterized equation which is regularized and penalized. The penalization is non-local in time and tracks the history of the system, penalizing the joint support of two different phases in space-time. The main result in the first paper is the existence theory of a weak solution to the parameterized equations in a Bochner space using the implicit function theorem. The family of solutions to the parameterized problem is uniformly bounded allowing us to extract a weakly convergent subsequence for the case when the penalization tends to infinity. The second problem deals with a parameterized highly oscillatory quasi-linear elliptic equation in divergence form. As the regularization parameter tends to zero the equation gets a jump in the conductivity which occur at the level set of a locally periodic function, the obstacle. As the oscillations in the problem data increases the solution to the equation experiences high frequency jumps in the conductivity, resulting in the corresponding solutions showing an effective global behaviour. The global behavior is related to the so called homogenized solution. We show that the parameterized equation has a weak solution in a Sobolev space and derive bounds on the solutions used in the analysis for the case when the regularization is lost. Surprisingly, the limiting problem in this case includes an extra term describing the interaction between the solution and the obstacle, not appearing in the case when obstacle is the zero level-set. The oscillatory nature of the problem makes standard numerical algorithms computationally expensive, since the global domain needs to be resolved on the micro scale. We develop a multi scale method for this problem based on the heterogeneous multiscale method (HMM) framework and using a finite element (FE) approach to capture the macroscopic variations of the solutions at a significantly lower cost. We numerically investigate the effect of the obstacle on the homogenized solution, finding empirical proof that certain choices of obstacles make the limiting problem have a form structurally different from that of the parameterized problem.

QC 20180222

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Книги з теми "Hele-Shaw problem":

Pugh, Mary Claire. Dynamics of interfaces of incompressible fluids: The Hele-Shaw problem. 1993.

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Частини книг з теми "Hele-Shaw problem":

Tani, Hisasi. "On Boundary Conditions for Hele-Shaw Problem." In Mathematical Analysis of Continuum Mechanics and Industrial Applications, 185–94. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2633-1_14.

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Fasano, A., and M. Primicerio. "Blow-Up and Regularization for the Hele-Shaw Problem." In Variational and Free Boundary Problems, 73–85. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4613-8357-4_6.

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Kuznetsov, Alexander. "A Note on Life-span of Classical Solutions to the Hele—Shaw Problem." In Analysis and Mathematical Physics, 369–76. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-9906-1_17.

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Tani, Atusi, and Hisasi Tani. "Classical Solvability of the Two-Phase Radial Viscous Fingering Problem in a Hele-Shaw Cell." In Mathematical Fluid Dynamics, Present and Future, 317–48. Tokyo: Springer Japan, 2016. http://dx.doi.org/10.1007/978-4-431-56457-7_11.

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Andreucci, Daniele, Giovanni Caruso, and Emmanuele DiBenedetto. "Ill-Posed Hele—Shaw Flows." In Free Boundary Problems, 27–51. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-7893-7_3.

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Meyer, Gunter H. "Front Tracking for the Unstable Hele-Shaw and Muskat Problems." In Flow in Porous Media, 129–37. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8564-5_12.

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Andreucci, D., A. Fasano, and M. Primicerio. "On the Occurrence of Singularities in Axisymmetrical Problems of Hele-Shaw Type." In Free Boundary Problems in Continuum Mechanics, 23–38. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8627-7_3.

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"2. The Hele–Shaw problem." In Free Boundaries in Rock Mechanics, 25–52. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110546163-003.

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"Chapter 26: Laplacian growth and Hele-Shaw flow." In Solving Problems in Multiply Connected Domains, 391–404. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2020. http://dx.doi.org/10.1137/1.9781611976151.ch26.

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"Computational Rheology and Applications." In Engineering Rheology, edited by Roger I. Tanner, 369–446. Oxford University PressOxford, 2000. http://dx.doi.org/10.1093/oso/9780198564737.003.0008.

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Abstract The mathematical complexity of rheological problems forces one to use computation for the effective solution of many problems arising in practice. That this is the case will be clear from studying the previous chapters, where simple flow fields were studied. For example, in fibre spinning one is led to numerical methods to determine the flow at exit from the spinneret (Fig. 7.7) even for a Newtonian fluid; the power-law analysis of the Hele-Shaw flow [Section 6.6.5, eqn (6.104)] is also generally beyond simple analytical techniques.

Тези доповідей конференцій з теми "Hele-Shaw problem":

Zhitnikov, Vladimir, Nataliya Sherykhalina, Aleksandra Sokolova, and Sergey Porechny. "Multi-Stage Filtering of Numerical Solutions With an Application to the Hele-Shaw Problem." In 8th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2020). Paris, France: Atlantis Press, 2020. http://dx.doi.org/10.2991/aisr.k.201029.034.

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Dupret, F., V. Verleye, and B. Languillier. "Numerical Prediction of the Molding of Composite Parts." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0476.

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Abstract This paper concerns the prediction of the effect of Hele Shaw flow upon the orientation of a suspension of short fibers. A numerical method to solve the decoupled free boundary flow problem and to calculate the fiber orientation is elaborated. Recent developments in the theory of the 3D natural closure approximation are presented and discussed.

Courbebaisse, G., D. Garcia, and P. Bourgin. "A Way Towards Optimization of Injection Molding." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45763.

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Injection molding of thermoplastic is a complex process essentially because of the physical properties of the polymers, the processing conditions and the mold geometry. One key issue is to find the optimal location of the injection point(s) so that to minimize the final pressure required to fill the mould. This is usually achieved by using commercial computer codes, which are time consuming. Our approach, which is not classical, consists in introducing several “geometrical tools” of image analysis such as optimal centering and skeleton transformation, to characterize the shape properties of the flow filling the mould cavity. A direct correlation between the geometrical parameters associated to image analysis and the results based on the classical Hele-Shaw model is obtained for several molds. Furthermore, the physical problem is not completely taken into account by the mathematical formulation based on the considered geometrical tools. It is the reason why a new formulation is proposed, taking the governing equations of the model into consideration. As the physical problem is of an elliptic form, its energetic formulation can be used to answer our problematic. In son doing, for a given fluid, the optimal position of the injection points can be found by writing a quadratic optimization problem. In this paper, we present the first results devoted to the optimization of the filling phase.

Etrati, Ali, and Ian Frigaard. "Laminar Displacement Flows in Vertical Eccentric Annuli: Experiments and Simulations." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95180.

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Abstract We present a numerical investigation of laminar miscible displacement flows in narrow, vertical, eccentric annuli. This study is motivated by the primary cementing stage of oil and gas well production, where successful displacement of drilling mud is crucial for the well integrity and zonal isolation. The large number of characterizing parameters makes a complete description of such flows challenging. In turn, this means that the design of effective strategies for primary cementing is a difficult task. As a result the existing literature is mostly based on non-inertial Hele-Shaw models and experiments in narrow annuli, where the dimensionality of the problem is reduced. In this preliminary study, we run a series of three-dimensional numerical simulations, using a Volume of Fluid (VOF) method to capture the interface between the fluids. Both Newtonian and non-Newtonian fluids are considered, and a variety of different phenomena are observed, e.g. dispersive spikes, static layers, instabilities and secondary flows. The range of flow parameters used in the simulations are similar to existing experimental data to allow for a preliminary comparison. The results show qualitative agreement with the experiments and gap-averaged models.

Kabanemi, Kalonji K., Jean-François Hétu, and Abdessalem Derdouri. "Design Sensitivity Analysis Applied to Injection Molding Process: Injection Pressure and Multi-Gate Location Optimization." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1223.

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Abstract In this work, we develop a numerical simulation method to optimize the injection molding process using the design sensitivity analysis (DSA). The optimization concerns the filling stage and focuses on the number and location of gates in a mold cavity as well as the injection pressure, considered as one of the key processing parameters, in order to minimize the fill time. Since the problem to be solved involves transient flow with free surfaces, the direct differentiation method is used to evaluate the sensitivities of the Hele-Shaw, filling fraction and the energy equations with respect to the design variables used in the analysis. The mesh domain parameterization is coped with using B-spline functions. Sensitivity equations are solved by means of finite element method. The proposed numerical approach is combined with the sequential linear and quadratic programming method of the DOT optimization tools to find the new design variables at each iteration. Starting with any initial gate locations and injection pressure profile, the method enables us to find the optimal gate locations together with the optimal injection pressure profile. Finally, numerical results involving complex mold geometries are presented and discussed to assess the validity and robustness of the proposed method.

Rai, S. N., and B. S. Bhadauria. "Heat/mass transport in walter-B nanoliquid filled in hele-shaw cell under 3-types of g-Jitters with magnetic field." In PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0201333.

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Kumar, Anish, and B. S. Bhadauria. "Nonlinear exploration of Oldroyd-B nano-liquid filled in hele-shaw cell under several types of gravity modulation with a thermal difference." In PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0201179.

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Dai, Q., Y. Meng, K. Duan, and C. Y. Kwok. "Development of Multiphase Flow Simulation Method in DEM Under a Fixed-Grain Condition." In 57th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2023. http://dx.doi.org/10.56952/arma-2023-0532.

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ABSTRACT Understanding multiphase flow mechanisms in porous media is vital for many engineering practices, such as geo-logical carbon sequestration. Existing numerical models that use the explicit pressure-solving scheme can only advance multiphase flow with a small timestep. None of them manages fast fluid transport due to a stability issue limiting timestep selection. This paper focuses on developing a fluid flow model that can quickly and efficiently capture fluid–fluid displacement patterns. We incorporate the implicit finite volume approach that is unconditionally stable to transport fluid with a remarkable timestep. To enhance interface–motion capture under various capillary number and viscosity ratio combinations, we set a flow front advancement criterion to reduce timestep when the injected fluid invades beyond front–line pores. Additionally, we update the flow front, pore pressure, and capillary entry pressure at every timestep to reveal more flow pattern details. We validate the model through a Darcy flow test and a fluid injection test based on existing Hele–Shaw tests. Numerical results agree well with the analytical solutions and experimental observations, confirming that the developed model is reliable for analyzing fluid migration problems and evaluating dynamic multiphase flow interactions in porous media. INTRODUCTION Geological CO2 sequestration is a crucial strategy for achieving carbon neutrality that stores greenhouse gas in geological formations, such as deep saline aquifers and depleted oil/gas reservoirs (Bradshaw et al., 2007; Bachu, 2008). Understanding how the injected CO2 migrates in geological media is vital to ensure successful CO2 geological storage. The injected CO2 will build up pore pressure and replace the existing pore fluid, remarkably altering the material properties (Sun et al., 2016) and pore structure (Yu et al., 2019). The pressure build-up during the injection process may trigger disasters, such as fault reactivation (White et al., 2014) and even earthquakes (Zoback and Gorelick, 2012), leading to CO2 leakage. To optimize CO2 injectivity and storage safety, it is thus essential to study multiphase flow mechanisms of fluid injection in porous media.