Tesi sul tema "Hele-Shaw problem"
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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.
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.
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/.
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/.
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.
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.
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.
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/.
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.
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.
QC 20180222
Runge, Vincent. "Eléments d'analyse et de contrôle dans le problème de Hele-Shaw". Thesis, Ecully, Ecole centrale de Lyon, 2014. http://www.theses.fr/2014ECDL0024/document.
This PhD thesis deals with the mathematical treatment of the Hele–Shaw problem in the Stokes–Leibenson approximation. By an Helmholtz–Kirchhoff transformation, we exhibited an evolutive equation of the fluid contour applicable to all type of planar fows. This equation generalizes previous results and also allows to state an efficient numerical scheme called quasi-contour’s, which is a simple Cauchy problem. We then consider the study of this problem using conformal transformations leading to the Polubarinova-Galin equation. In the simple case of a contour representing by a trinomial with real coefficients, we succeeded in exhibiting the exact solution of the problem. Notice that the trajectories of the exact solutions enable to precise the position of frontiers of univalent domains described by trinomials. Finally, we introduce control parameters under the form of coefficients of a multipole superposed to the source. Sufficient conditions of controllability are stated and results on optimal control established for the binomial and trinomial cases. Introduction of control parameters allows us to understand the link, which bound Richardson’s moments to the Polubarinova-Galin equation
Egly, Hugues. "Contribution à la modélisation et à la simulation des instabilités de type Rayleigh-Taylor ablatif pour la FCI". Paris 6, 2007. http://www.theses.fr/2007PA066684.
This thesis deals with the dynamics of accelerated ablative front spreading in Inertial Confinement Fusion experiments. ICF is designed for the implosion of a mdeuterium or tritium spherical target. The outer shell, the ablator, is irradiated providing a high level pressure inside the target. During this first stage, the ablation front propagating inward is perturbed by hydrodynamics instabilities, which can prevent the fusion reaction in the decelerated stage. We propose here a study on Rayleigh-Taylor instabilities during ablation process, in the two dimensional case. In order to obtain a numerical solution, we perform an asymptotic analysis in the limit of a high temperature ratio, between the remaining cold ablator and the hot ablated plasma. This study is divided in two steps. First, the thermo-diffusive part of the set of equations is approximated by a Hele-Shaw model, which is then perturbed by the hydrodynamics part. Using a vortex method, we have to solve the advection of a vortical sheet moving with the ablation front. We compute the numerical solution on an eulerian mesh coupled with a front tracking method. The thermal part is calculated by implementing the Fat Boundary Method, recently developped. The hydrodynamic part is obtained from a Finit Volume scheme
Pauné, i. Xuriguera Eduard. "Interface Dynamics in Two-dimensional Viscous Flows". Doctoral thesis, Universitat de Barcelona, 2002. http://hdl.handle.net/10803/1584.
underlying the physics of interface dynamics, which we hope will exhibit some degree of universality. The aim is twofold: on the one hand we focus on the role of surface tension and viscosity contrast in the dynamics of fingering patterns. On the other hand we introduce a modification of the original problem and study the effects of a inhomogeneous gap between the
plates of a Hele-Shaw cell.
A dynamical systems approach to competition of Saffman-Taylor (ST) fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the ODE sets associated to the exact solutions of the problem without surface tension. A general proof of the existence of finite-time singularities for broad classes of solutions is given. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic. Hyperbolicity (saddle-point structure) of multifinger fixed points is argued to be essential to the physically correct qualitative
description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic Dynamical Solvability Scenario for interfacial pattern selection.
We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques developed by Tanveer and Siegel, and numerical computation, following the numerical scheme of Hou, Lowengrub, and
Shelley. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact
(non-singular) zero-surface tension solutions. The effect is present even when the zero surface tension solution has asymptotic behavior consistent with selection theory. Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow.
Finger competition with arbitrary viscosity contrast (or Atwood ratio) is
studied by means of numerical computation. Two different types of dynamics
are observed, depending on the value of the viscosity contrast an the
initial condition. One of them exhibits finger competition and ends up in
the ST finger. In opposition, the second dynamics does not exhibit finger
competition and the long time dynamics seems attracted to bubble shaped
solutions. An initial condition appropriate to study the ST finger basin
of attraction is identified, and used to characterize its dependence on
the viscosity contrast, obtaining that its size decreases for decreasing
viscosity contrast, being very small for zero viscosity contrast. The ST
finger is not the universal attractor for arbitrary viscosity contrast. An
alternative class of attractors is identified as the set of Taylor-Saffman
bubble solutions, and one important implication of this result is that the
interface is strongly attracted to finite time pinchoff.
A nonlocal interface equation is derived for two-phase fluid flow, with
arbitrary wettability and viscosity contrast c, in a model porous medium defined as a Hele-Shaw cell with random gap b. Fluctuations of both capillary and viscous pressure are explicitly related to the microscopic quenched disorder, yielding conserved, non-conserved and power-law correlated noise terms. Two length scales are identified that control the possible scaling regimes and which depend on capillary number Ca as l sub 1 = b sub zero (c Ca)(superindex -1/2) and l sub 2 = b sub zero/Ca. Exponents for forced fluid invasion are obtained from numerical simulation and compared with recent experiments,obtaining good partial agreement.
Guillen, Nestor Daniel. "Regularization in phase transitions with Gibbs-Thomson law". Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-12-2562.
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PEZZA, Laura. "Su un modello di Hele-Shaw dipendente dalla temperatura". Doctoral thesis, 1996. http://hdl.handle.net/11573/484674.
We constructed a model for the injection of a fluid in a Hele-Shaw cell and we study the properties of existence and uniqueness of the differential problem solution. These equations are of parabolic and transport kind, with an integral differential condition on the interface.