Tesi sul tema "Limite incompressible"
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Casalis, Grégoire. "Instabilites primaire et secondaire dans la couche limite laminaire pour un fluide incompressible". Paris 6, 1990. http://www.theses.fr/1990PA066068.
Walther, Steeve. "Sensibilité et contrôle optimal des ondes TS dans une couche limite incompressible de plaque plane". Toulouse 3, 2001. http://www.theses.fr/2001TOU30170.
Copie, Marie-Laurence. "Stabilité linéaire et faiblement non linéaire d'une couche limite pour un fluide incompressible avec l'approche PSE". Toulouse, ENSAE, 1996. http://www.theses.fr/1996ESAE0006.
Airiau, Christophe. "Stabilité linéaire et faiblement non linéaire d'une couche limite laminaire incompressible par un système d'équations parabolisé (PSE)". Toulouse, ENSAE, 1994. http://www.theses.fr/1994ESAE0023.
Cathalifaud, Patricia. "Etude de l'amplification de tourbillons longitudinaux, et contole de la perturbation optimale dans une couche limite incompressible". Toulouse 3, 2000. http://www.theses.fr/2000TOU30080.
Sharifi, Tashnizi Ebrahim. "Contribution à l'étude de la couche limite turbulente et de son décollement dans les diffuseurs plan et à symétrie de révolution". Valenciennes, 2000. https://ged.uphf.fr/nuxeo/site/esupversions/452fe014-da49-425a-85c0-c44ce149ed5a.
Bravin, Marco. "Dynamics of a viscous incompressible flow in presence of a rigid body and of an inviscid incompressible flow in presence of a source and a sink". Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0192.
In this thesis, we investigate properties of incompressible flows that interact with a rigid body or a source and a sink. In the case of an incompressible viscous fluid that satisfies the Navier Stokes equations in a 2D bounded domain well-posedness of Leray-Hopf weak solutions is well-understood. Existence and uniqueness are proved. Moreover solutions are continuous in time with values in L 2 (Omega) and they satisfy the energy equality. Recently the problem of a rigid body moving in a viscous incompressible fluid modeled by the Navier-Stokes equations coupled with the Newton laws that prescribe the motion of the solid, was also tackled in the case where the no-slip boundary conditions were imposed. And the correspondent well-posedness result for Leray-Hopf type weak solutions was proved. In this manuscript we consider the case of the Navier-slip boundary conditions. In this setting, the existence result for the coupled system was proved by G'erard-Varet and Hillairet in 2014. Here, we prove that solutions are continuous in time, that they satisfy the energy equality and that they are unique. Moreover we show an existence result for weak solutions of a viscous incompressible fluid plus rigid body system in the case where the fluid velocity has an orthoradial part of infinite energy.For an inviscid incompressible fluid modelled by the Euler equations in a 2D bounded domain, the case where the fluid is allowed to enter and to exit from the boundary was tackled by Judovic who introduced some conditions which consist in prescribing the normal component of the velocity and the entering vorticity. In this manuscript we consider a bounded domain with two holes, one of them is a source which means that the fluid is allowed to enter in the domain and the other is a sink from where the fluid can exit. In particular we find the limiting equations satisfied by the fluid when the source and the sink shrink to two different points. The limiting system is characterized by a point source/sink and a point vortex in each of the two points where the holes shrunk
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
Evrard, Jean. "Étude des fluctuations de vitesse et de pression en régime laminaire et dans la région de transition en écoulement bidimensionnel incompressible". Toulouse, ENSAE, 1989. http://www.theses.fr/1989ESAE0008.
Derebail, Muralidhar Srikanth. "Instabilité de l'écoulement le long d'un cylindre semi-infini en rotation". Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEC033/document.
This work concerns the steady, incompressible flow around a semi-infinite, rotating cylinder and its linear-stability properties. The effect of cylinder curvature and rotation on the stability of this flow is investigated in a systematic manner. Prior to studying its stability, we first compute the basic flow. At large Reynolds numbers, a boundary layer develops along the cylinder. The governing equations are obtained using a boundary-layer approximation to the Navier–Stokes equations. These equations contain two non-dimensional control parameters: the Reynolds number (Re) and the rotation rate (S), and are numerically solved to obtain the velocity and pressure profiles for a wide range of control parameters. The initially thin boundary layer grows in thickness with axial distance, becoming comparable and eventually larger than the cylinder radius. Above a threshold rotation rate, a centrifugal effect leads to the presence of a wall jet for a certain range of streamwise distances. This range widens as the rotation rate increases. Furthermore, the wall jet strengthens as S increases. Asymptotic analyses of the flow at large streamwise distances and at large rotation rates are presented. A linear stability analysis of the above flow is carried out using a local-flow approximation. Upon normal-mode decomposition, the perturbation equations are transformed to an eigenvalue problem in complex frequency (ω). The problem depends on five non-dimensional parameters: Re, S, scaled streamwise direction (Z), streamwise wavenumber (α) and azimuthal wavenumber m. The stability equations are numerically solved to investigate the unstable regions in parameter space. It is found that small amounts of rotation have strong effects on flow stability. Strong destabilization by small rotation is associated with the presence of a nearly neutral mode of the non-rotating cylinder, which becomes unstable at small S. This is further quantified using smallS perturbation theory. In the absence of rotation, the flow is stable for all Re below 1060, and for Z above 0.81. However, in the presence of small rotation, the instability becomes unconstrained by a minimum Re or a threshold in Z. The critical curves in the (Z, Re) plane are computed for a wide range of S and the consequences for stability of the flow described. Finally, a large-Z asymptotic expansion of the critical Reynolds number is obtained
Martínez, Germán Andrés Gaviria. "Towards natural transition in compressible boundary layers". Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/18/18148/tde-24052017-114027/.
No presente trabalho, um código DNS (Direct Numerical Simulation) foi desenvolvido para abordar problemas de transição para turbulência em camada limite subsônica compressível em uma placa plana. Foram realizados testes de validação de código , nos regimes linear e não linear do processo de transição, nos regimes incompressível e compressível. O foco do presente trabalho é estudar transição natural modelada por meio de pacotes de onda em camada limite compressível subsônica, e realizar uma análise preliminar da transição induzida por ruído branco. Três assuntos principais foram considerados: uma simulação DNS e uma análise comparativa com o experimento (MEDEIROS; GASTER, 1999b) sobre a evolução de um pacote de ondas em camada limite incompressível, a influência da compressibilidade na evolução de pacotes de ondas no regime subsônico, e por último, um estudo preliminar da transição induzida por ruído branco em Mach 0.2 e Mach 0.9. As comparações realizadas entre a solução numérica e os dados experimentais mostram uma boa concordância, nos regimes linear e não linear, tanto no espaço físico quanto no espaço de Fourier. A simulação numérica deste experimento e a análise realizada neste trabalho, não são encontradas na literatura para o regime incompressível. A análise modal não linear aplicada aos resultados, permitiu identificar a presença das ressonâncias tipo H e tipo K no pacote de ondas. A influência da compressibilidade na evolução dos pacotes de onda foi estudada em Mach 0.7 e Mach 0.9. Na literatura não há trabalhos sobre pacotes de ondas no regime sub- sônico. No regime linear da transição, os modos oblíquos resultam ser os mais instáveis para Mach > 0.7, como era de esperar, de acordo com os resultados da literatura. No regime não linear, foram observadas estrias de moderada amplitude, associadas com modos de baixa frequência que acabam decaindo. O pacote de ondas em Mach 0.9 apresentou amplificação não linear somente na banda subharmônica, que pode ser associada com transição tipo H ou ressonância dessintonizada. No entanto, o comportamento geral neste regime é estabilizante. Por sua vez, a interação entre pacotes de ondas em Mach 0.9 mostrou um comportamento desestabilizante, pois a interação acaba gerando amplificação não linear em modos que decaem no pacote isolado. Os modos amplificados sugerem a presença do mecanismo de transição oblíqua. Finalmente, a evolução da mesma perturbação constituída por ruído branco em Mach 0.2 e Mach 0.9, resultaram ser completamente diferentes. Na camada limite incompressível foram observados vórtices tipo lambda, que poderiam ser gerados pela presença localizada das ressonâncias tipo H e/ou tipo K. No regime compressível foram observados vórtices distribuidos em todo o domínio, o que sugere a presença da transição oblíqua. Na transição gerada por ruído branco a compressibilidade teve uma influência maior que no pacote de ondas. Nas condições estudadas, a interação entre pacotes de ondas parece ser uma melhor representação do ruído branco no regime compressível.
Lin, Chi-Kun. "On the incompressible limit of the compressible Navier-Stokes equations". Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185888.
Kadri, Harouna Souleymane. "Ondelettes pour la prise en compte de conditions aux limites en turbulence incompressible". Grenoble, 2010. http://www.theses.fr/2010GRENM050.
This work concerns wavelet numerical methods for the simulation of incompressible turbulent flow. The main objective of this work is to take into account physical boundary conditions in the resolution of Navier-Stokes equations on wavelet basis. Unlike previous work where the vorticity field was decomposed in term of classical wavelet bases, the point of view adopted here is to compute the velocity field of the flow in its divergence-free wavelet series. We are then in the context of velocity-pressure formulation of the incompressible Navier-Stokes equations, for which the boundary conditions are written explicitly on the velocity field, which differs from the velocity-vorticity formulation. The principle of the method implemented is to incorporate directly the boundary conditions on the wavelet basis. This work extends the work of the thesis of E. Deriaz realized in the periodic case. The first part of this work highlights the definition and the construction of new divergence-free and curl-free wavelet bases on [0,1]n, which can take into account boundary conditions, from original works of P. G. Lemarie-Rieusset, K. Urban, E. Deriaz and V. Perrier. In the second part, efficient numerical methods using these new wavelets are proposed to solve various classical problem: heat equation, Stokes problem and Helmholtz-Hodge decomposition in the non-periodic case. The existence of fast algorithms makes the associated methods more competitive. The last part is devoted to the definition of two new numerical schemes for the resolution of the incompressible Navier-Stokes equations into wavelets, using the above ingredients. Numerical experiments conducted for the simulation of driven cavity flow in two dimensions or the issue of reconnection of vortex tubes in three dimensions show the strong potential of the developed algorithms
Leroy, Agnes. "Un nouveau modèle SPH incompressible : vers l’application à des cas industriels". Thesis, Paris Est, 2014. http://www.theses.fr/2014PEST1065/document.
In this work a numerical model for fluid flow simulation was developed, based on the Smoothed Particle Hydrodynamics (SPH) method. SPH is a meshless Lagrangian Computational Fluid Dynamics (CFD) method that offers some advantages compared to mesh-based Eulerian methods. In particular, it is able to model flows presenting highly distorted free-surfaces or interfaces. This work tackles four issues concerning the SPH method : the imposition of boundary conditions, the accuracy of the pressure prediction, the modelling of buoyancy effects and the reduction of computational time. The aim is to model complex industrial flows with the SPH method, as a complement of what can be done with mesh-based methods. Typically, the targetted problems are 3-D free-surface or confined flows that may interact with moving solids and/or transport scalars, in particular active scalars (e.g. the temperature). To achieve this goal, a new incompressible SPH (ISPH) model is proposed, based on semi-analytical boundary conditions. This technique for the representation of boundary conditions in SPH makes it possible to accurately prescribe consistent pressure boundary conditions, contrary to what is done with classical boundary conditions in SPH. A k-epsilon turbulence closure is included in the new ISPH model. A buoyancy model was also added, based on the Boussinesq approximation. The interactions between buoyancy and turbulence are modelled. Finally, a formulation for open boundary conditions is proposed in this framework. The 2-D validation was performed on a set of test-cases that made it possible to assess the prediction capabilities of the new model regarding isothermal and non-isothermal flows, in laminar or turbulent regime. Confined cases are presented, as well as free-surface flows (one of them including a moving body in the flow). The open boundary formulation was tested on a laminar plane Poiseuille flow and on two cases of propagation of a solitary wave. Comparisons with mesh-based methods are provided with, as well as comparisons with a weakly-compressible SPH (WCSPH) model using the same kind of boundary conditions. The results show that the model is able to represent flows in complex boundary geometries, while improving the pressure prediction compared to the WCSPH method. The extension of the model to 3-D was done in a massively parallel code running on a Graphic Processing Unit (GPU). Two validation cases in 3-D are presented, as well as preliminary results on a simple 3-D application case
Lohéac, Jean-Pierre. "Conditions aux limites artificielles pour des modèles de la mécanique des fluides". Lyon 1, 1989. http://www.theses.fr/1989LYO19009.
Sallaberry, Cédric. "Simulation directe d'écoulements incompressibles en dimensions deux et trois". Bordeaux 1, 2001. http://www.theses.fr/2001BOR12377.
Chantalat, Frédéric. "Méthodes level-set et de pénalisation pour l'optimisation et le contrôle d'écoulements". Thesis, Bordeaux 1, 2009. http://www.theses.fr/2009BOR13828/document.
This work deals with e?cient numerical solving of problems linked with shape optimization or ?ow control. The combination between penalization, that allows to impose boundary conditions while avoiding the use of body-?tted grids, and Level-Set methods, which enable a natural non-parametric representation of the geometries to be optimized, is implemented. In the ?rst part, a model inverse problem, and an application pertaining to optimal design in Stokes ?ows, are treated with an iterative algorithm. Special care is devoted to the solution of the PDE’s in the vicinity of the penalized regions. The discretization accuracy is increased. Various gradient preconditionings aiming at improving the convergence are also discussed. The second part is dedicated to direct numerical simulation of ?ows in the neighborhood of an actuator, in the context of active control by pulsed jets used on the Ahmed body. The local study emphasizes the in?uence of various parameters on the action quality, in particular the pulsation frequency, or the aspect of exit velocity pro?les. As a synthesis, shape optimization is performed on the actuator of chapter two, thanks to the previously introduced coupling between Level-Set and penalization. The framework is simpli?ed and topological constraints are imposed. The inverse problem we set intends to modify the MEMS inner geometry to retrieve a given jet pro?le on the exit section
ARGENZIANO, Andrea. "The inviscid limit and Prandtl's asymptotic expansion for incompressible flows in the half space". Doctoral thesis, Università degli Studi di Palermo, 2022. https://hdl.handle.net/10447/554200.
Pares, Madronal Carlos. "Etude mathématique et approximation numérique de quelques problèmes aux limites de la mécanique des fluides incompressibles". Paris 6, 1991. http://www.theses.fr/1991PA066600.
Vermeersch, Olivier. "Étude et modélisation du phénomène de croissance transitoire pour des couches limites incompressibles et compressibles". Toulouse, ISAE, 2009. http://www.theses.fr/2009ESAE0022.
Laburthe, François. "Problème de stabilité linéaire et prévision de la transition dans des configurations tridimensionnelles, incompressibles et compressibles". Toulouse, ENSAE, 1992. http://www.theses.fr/1992ESAE0019.
HIENTZSCH, LARS ERIC. "Non linear Schrödinger equations and quantum fluids non vanishing at infinity: incompressible limits and quantum vortices". Doctoral thesis, Gran Sasso Science Institute, 2019. https://hdl.handle.net/20.500.12571/26564.
Nguyen, Thi-Hien. "Etude de l'asymptotique du phénomène d'augmentation de diffusivité dans des flots à grande vitesse". Thesis, Brest, 2017. http://www.theses.fr/2017BRES0072/document.
In application, we would like to generate random numbers with a precise law MCMC (Markov Chaine Monte Carlo). The method consists in finding a diffusion which has the desired invariant law and in showing the convergence of this diffusion towards its equilibrium with an exponential rate. The exponent of this convergence is the spectral gap of the generator. It was shown by C.-R. Hwang, S.-Y. Hwang-Ma and S.-J. Sheu that the spectral gap can grow up by adding a non-symmetric term to the self-adjoint generator.This corresponds to passing from a reversible diffusion to a non-reversible diffusion. A means of constructing a non-reversible diffusion with the same invariant measure is to add an incompressible flow to the dynamics of the reversible diffusion.In this thesis, we study the behavior of diffusion when the flow is accelerated by multiplying the field of the vectors which describes it by a large constant. In 2008, P. Constantin, A. Kisekev, L. Ryzhik and A. Zlatoˇs have shown that if the flow was weakly mixing then the acceleration of the flow was sufficient to converge the diffusion towards its equilibrium after finite time. In this work, the speed of this phenomenon is explained under a condition of correlation of the flow. The article by B. Franke, C.-R.Hwang, H.-M. Pai and S.-J.Sheu (2010) gives the asymptotic expression of the spectral gap when the large constant goes to infinity. Here we are also interested in the speed with which the phenomenon manifests itself. First, we study the special case of an Ornstein-Uhlenbeck diffusion which is perturbed by a flow preserving the Gaussian measure. In this case, thanks to a result of G. Metafune, D. Pallara and E. Priola (2002), we can reduce the study of the generator spectrum to eigenvalues of a family of matrices. We study this problem with methods of limited development of eigenvalues. This problem is solved explicitly in this thesis and we also give a boundary for the convergence radius of the development. We then generalize this method in the case of a general diffusion in a formal way. These results may be useful to have a first idea on the speeds of convergence of the spectral gap described in the article by Franke et al. (2010)
Abidi, Hammadi. "Etude mathématique de quelques problèmes de mécanique des fluides incompressibles". Paris 6, 2004. http://www.theses.fr/2004PA066346.
Jelliti, Miloud. "Transition du régime laminaire au régime turbulent : effets de la tridimensionnalité et de la compressibilité". Toulouse, ENSAE, 1986. http://www.theses.fr/1986ESAE0005.
Bocchi, Edoardo. "Compressible-incompressible transitions in fluid mechanics : waves-structures interaction and rotating fluids". Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0279/document.
This manuscript deals with compressible-incompressible transitions arising in partial differential equations of fluid mechanics. We investigate two problems: floating structures and rotating fluids. In the first problem, the introduction of a floating object into water waves enforces a constraint on the fluid and the governing equations turn out to have a compressible-incompressible structure. In the second problem, the motion of geophysical compressible fluids is affected by the Earth's rotation and the study of the high rotation limit shows that the velocity vector field tends to be horizontal and with an incompressibility constraint.Floating structures are a particular example of fluid-structure interaction, in which a partially immersed solid is floating at the fluid surface. This mathematical problem models the motion of wave energy converters in sea water. In particular, we focus on heaving buoys, usually implemented in the near-shore zone, where the shallow water asymptotic models describe accurately the motion of waves. We study the two-dimensional nonlinear shallow water equations in the axisymmetric configuration in the presence of a floating object with vertical side-walls moving only vertically. The assumptions on the solid permit to avoid the free boundary problem associated with the moving contact line between the air, the water and the solid. Hence, in the domain exterior to the solid the fluid equations can be written as an hyperbolic quasilinear initial boundary value problem. This couples with a nonlinear second order ODE derived from Newton's law for the free solid motion. Local in time well-posedness of the coupled system is shown provided some compatibility conditions are satisfied by the initial data in order to generate smooth solutions.Afterwards, we address a particular configuration of this fluid-structure interaction: the return to equilibrium. It consists in releasing a partially immersed solid body into a fluid initially at rest and letting it evolve towards its equilibrium position. A different hydrodynamical model is used. In the exterior domain the equations are linearized but the nonlinear effects are taken into account under the solid. The equation for the solid motion becomes a nonlinear second order integro-differential equation which rigorously justifies the Cummins equation, assumed by engineers to govern the motion of floating objects. Moreover, the equation derived improves the linear approach of Cummins by taking into account the nonlinear effects. The global existence and uniqueness of the solution is shown for small data using the conservation of the energy of the fluid-structure system.In the second part of the manuscript, highly rotating fluids are studied. This mathematical problem models the motion of geophysical flows at large scales affected by the Earth's rotation, such as massive oceanic and atmospheric currents. The motion is also influenced by the gravity, which causes a stratification of the density in compressible fluids. The rotation generates anisotropy in viscous flows and the vertical turbulent viscosity tends to zero in the high rotation limit. Our interest lies in this singular limit problem taking into account gravitational and compressible effects. We study the compressible anisotropic Navier-Stokes-Coriolis equations with gravitational force in the horizontal infinite slab with no-slip boundary condition. Both this condition and the Coriolis force cause the apparition of Ekman layers near the boundary. They are taken into account in the analysis by adding corrector terms which decay in the interior of the domain. In this work well-prepared initial data are considered. A stability result of global weak solutions is shown for power-type pressure laws. The limit dynamics is described by a two-dimensional viscous quasi-geostrophic equation with a damping term that accounts for the boundary layers
Cheaytou, Rima. "Etude des méthodes de pénalité-projection vectorielle pour les équations de Navier-Stokes avec conditions aux limites ouvertes". Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4715.
Motivated by solving the incompressible Navier-Stokes equations with open boundary conditions, this thesis studies the Vector Penalty-Projection method denoted VPP, which is a splitting method in time. We first present a literature review of the projection methods addressing the issue of the velocity-pressure coupling in the incompressible Navier-Stokes system. First, we focus on the case of Dirichlet conditions on the entire boundary. The numerical tests show a second-order convergence in time for both the velocity and the pressure. They also show that the VPP method is fast and cheap in terms of number of iterations at each time step. In addition, we established for the Stokes problem optimal error estimates for the velocity and pressure and the numerical experiments are in perfect agreement with the theoretical results. However, the incompressibility constraint is not exactly equal to zero and it scales as O(varepsilondelta t) where $varepsilon$ is a penalty parameter chosen small enough and delta t is the time step. Moreover, we deal with the natural outflow boundary condition. Three types of outflow boundary conditions are presented and numerically tested for the projection step. We perform quantitative comparisons of the results with those obtained by other methods in the literature. Besides, a theoretical study of the VPP method with outflow boundary conditions is stated and the numerical tests prove to be in good agreement with the theoretical results. In the last chapter, we focus on the numerical study of the VPP scheme with a nonlinear open artificial boundary condition modelling a singular load for the unsteady incompressible Navier-Stokes problem
Chandesris, Marion. "Modélisation des écoulements turbulents dans les milieux poreux et à l'interface avec un milieu libre". Paris 6, 2006. http://www.theses.fr/2006PA066456.
Scandurra, Leonardo. "Numerical Methods for All Mach Number flows for Gas Dynamics". Doctoral thesis, Università di Catania, 2017. http://hdl.handle.net/10761/4042.
Jobic, Yann. "Numerical approach by kinetic methods of transport phenomena in heterogeneous media". Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4723/document.
A novel kinetic scheme satisfying an entropy condition is developed, tested and implemented for the simulation of practical problems. The construction of this new entropic scheme is presented. A classical hyperbolic system is approximated by a discrete velocity vector kinetic scheme (with the simplified BGK collisional operator), but applied to an inviscid compressible gas dynamics system with a small Mach number parameter, according to the approach of Carfora and Natalini (2008). The numerical viscosity is controlled, and tends to the physical viscosity of the Navier-Stokes system. The proposed numerical scheme is analyzed and formulated as an explicit finite volume flux vector splitting (FVS) scheme that is very easy to implement. It is close in spirit to Lattice Boltzmann schemes, but it has the advantage to satisfy a discrete entropy inequality under a CFL condition and a subcharacteristic stability condition involving a cell Reynolds number. The new scheme is proved to be second-order accurate in space. We show the efficiency of the method in terms of accuracy and robustness on a variety of classical benchmark tests. Some physical problems have been studied in order to show the usefulness of both schemes. The LB code was successfully used to determine the longitudinal dispersion of metallic foams, with the use of a novel indicator. The entropic code was used to determine the permeability tensor of various porous media, from the Fontainebleau sandstone (low porosity) to a redwood tree sample (high porosity). These results are pretty accurate. Finally, the entropic framework is applied to the advection-diffusion equation as a passive scalar
Miot, Evelyne. "Quelques problèmes relatifs à la dynamique des points vortex dans les équations d'Euler et de Ginzburg-Landau complexe". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2009. http://tel.archives-ouvertes.fr/tel-00444820.
Kelliher, James Patrick Vishik Mikhail M. "The vanishing viscosity limit for incompressible fluids in two dimensions". 2005. http://repositories.lib.utexas.edu/bitstream/handle/2152/1589/kelliherj01219.pdf.
Kelliher, James Patrick. "The vanishing viscosity limit for incompressible fluids in two dimensions". Thesis, 2005. http://hdl.handle.net/2152/1589.
Kadri, Harouna Souleymane. "Ondelettes pour la prise en compte de conditions aux limites en turbulence incompressible". Phd thesis, 2010. http://tel.archives-ouvertes.fr/tel-00544373.
Ming-Yuan, Wu. "Compressible and Incompressible Limits of Coupled Systems of Nonlinear Schrodinger Equation with Trap Potentials". 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-1807200617274000.
Wu, Ming-Yuan, e 吳銘原. "Compressible and Incompressible Limits of Coupled Systems of Nonlinear Schrodinger Equation with Trap Potentials". Thesis, 2006. http://ndltd.ncl.edu.tw/handle/26729188161329912543.
國立臺灣大學
數學研究所
94
We add the trap potentials based on coupled systems of nonlinear Schrodinger equation in the previous paper, and use these to conjecture possible effect of compressible and incompressible limits. The main idea of our arguments is to define an ``H-function'', to prove some conservation laws, and to calculate for result after substitution. There are four sections in this paper. In Section 1, we write the equations discussed in the main bibliography. Moreover, we discuss the result after adding one term(trap potential), and conclude the outcome. In Section 2, we prove some conservation laws. According to these,we prove the two main theorem in Section 3 and Section 4.
麥顥覺. "A thermal lattice Boltzmann model for flows with viscous heat dissipation in the incompressible limit". Thesis, 2009. http://ndltd.ncl.edu.tw/handle/01106675333879486045.
Su, Cheng-Fang, e 蘇承芳. "The well-posedness of Navier-Stokes equations and the incompressible limit of rotational compressible magnetohydrodynamic flows". Thesis, 2018. http://ndltd.ncl.edu.tw/handle/xq4738.
國立中央大學
數學系
106
There are two sub-projects in this dissertation: one is the problem of the incompressible limits for rotational compressible MHD flows and another is the well-posedness of Navier-Stokes equations with surface tension in an optimal Sobolev space. In the first sub-project, we consider the compressible models of magnetohydrodynamic flows which gives rise to a variety of mathematical problems in many areas. We introduce the asymptotic limit for the compressible rotational magnetohydrodynamic flows with the well-prepared initial data such that a rigorous quasi-geostrophic equation with diffusion term governed by the magnetic field from a compressible rotational magnetohydrodynamic flows is derived. After that, we show the two results: the existence of the unique global strong solution of quasi-geostrophic equation with good regularity on the velocity and magnetic field and the derivation of quasi-geostrophic equation with diffusion. In the second sub-project, we establish the existence of a solution to the 2-dimensional Navier-Stokes equations with surface tension on a moving domain. To deal with the free boundary problem, we adopt the ALE formulation which transform the moving domain into a fixed domain. Next, we show the well-posedness of this systems in an optimal sobolev space and no compatibility conditions are required to guarantee the existence of a solution.
Dębiec, Tomasz. "Weak convergence methods for equations of mathematical physics and biology". Doctoral thesis, 2020. https://depotuw.ceon.pl/handle/item/3775.
Niniejsza rozprawa stanowi zbiór wyników dotyczących matematycznej analizy pewnych równań różniczkowych cząstkowych motywowanych zagadnieniami fizyki i biologii matematycznej. Tematy, które badamy, są różnorodne ze względu na własności jakościowe oraz zastosowania – jednakże wspólną ich cechą jest potrzeba starannego rozwijania całego wachlarza metod słabej zbieżności i zwartości, nieodzownych przy analizie zjawisk nieliniowych. W pierwszej części rozprawy badamy związek pomiędzy regularnością a wielkościami zachowywanymi dla pewnych równań obecnych w mechanice płynów. Głównymi wynikami są tutaj warunki wystarczające do zapewnienia spełnienia lokalnej równości energetycznej przez słabe rozwiązania układu Eulera-Kortewega, oraz ściśliwego układu Eulera (a również Naviera-Stokesa) w zdegenerowanym przypadku występowania obszarów próżni. Następnie badamy podstawowe równanie w dziedzinie dynamiki populacji ze strukturą, a mianowicie równanie wzrostu-podziału. Jest to liniowe równanie całkowo-różniczkowe opisujące współzawodnictwo pomiędzy procesami wzrostu komórkowego a fragmentacją. Głównym wynikiem tej części rozprawy jest wykazanie, że rozwiązanie pochodzące z danych początkowych w przestrzeni nieujemnych miar Radona zbiega, w odpowiedniej normie z wagą, do stanu stacjonarnego. W ostatniej części rozprawy rozważamy dwugatunkowy model motywowany zastosowaniami w opisie wzrostu komórek nowotworowych. Równania zadające dynamikę obu gatunków są sprzężone poprzez prawo Brinkmana, tj. równanie eliptyczne wiążące ich prędkość z ciśnieniem, które jest z kolei proporcjonalne do potęgi całkowitej gęstości populacji. Uzyskane wyniki dotyczą istnienia oraz jednoznaczności słabych rozwiązań układu, oraz przejścia asymptotycznego z wykładnikiem zadającym związek pomiędzy ciśnieniem a całkowitą populacją. Ukazuje to powiązanie rozważanego modelu z geometrycznym modelem o swobodnym brzegu.