Relevant bibliographies by topics / Approximation de Boussinesq quadratique

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Academic literature on the topic 'Approximation de Boussinesq quadratique'

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Published: 7 December 2024

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Journal articles on the topic "Approximation de Boussinesq quadratique"

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Young, William R. "Dynamic Enthalpy, Conservative Temperature, and the Seawater Boussinesq Approximation." Journal of Physical Oceanography 40, no. 2 (February 1, 2010): 394–400. http://dx.doi.org/10.1175/2009jpo4294.1.

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Abstract A new seawater Boussinesq system is introduced, and it is shown that this approximation to the equations of motion of a compressible binary solution has an energy conservation law that is a consistent approximation to the Bernoulli equation of the full system. The seawater Boussinesq approximation simplifies the mass conservation equation to ∇ · u = 0, employs the nonlinear equation of state of seawater to obtain the buoyancy force, and uses the conservative temperature introduced by McDougall as a thermal variable. The conserved energy consists of the kinetic energy plus the Boussinesq dynamic enthalpy h‡, which is the integral of the buoyancy with respect to geopotential height Z at a fixed conservative temperature and salinity. In the Boussinesq approximation, the full specific enthalpy h is the sum of four terms: McDougall’s potential enthalpy, minus the geopotential g0Z, plus the Boussinesq dynamic enthalpy h‡, and plus the dynamic pressure. The seawater Boussinesq approximation removes the large and dynamically inert contributions to h, and it reveals the important conversions between kinetic energy and h‡.
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Wood, T. S., and P. J. Bushby. "Oscillatory convection and limitations of the Boussinesq approximation." Journal of Fluid Mechanics 803 (August 30, 2016): 502–15. http://dx.doi.org/10.1017/jfm.2016.511.

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We determine the asymptotic conditions under which the Boussinesq approximation is valid for oscillatory convection in a rapidly rotating fluid. In the astrophysically relevant parameter regime of small Prandtl number, we show that the Boussinesq prediction for the onset of convection is valid only under much more restrictive conditions than those that are usually assumed. In the case of an ideal gas, we recover the Boussinesq results only if the ratio of the domain height to a typical scale height is much smaller than the Prandtl number. This requires an extremely shallow domain in the astrophysical parameter regime. Other commonly used ‘sound-proof’ approximations generally perform no better than the Boussinesq approximation. The exception is a particular implementation of the pseudo-incompressible approximation, which predicts the correct instability threshold beyond the range of validity of the Boussinesq approximation.
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RAJAGOPAL, K. R., M. RUZICKA, and A. R. SRINIVASA. "ON THE OBERBECK-BOUSSINESQ APPROXIMATION." Mathematical Models and Methods in Applied Sciences 06, no. 08 (December 1996): 1157–67. http://dx.doi.org/10.1142/s0218202596000481.

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This paper deals with a derivation (using a perturbation technique) of an approximation, due to Oberbeck8,9 and Boussinesq,1 to describe the thermal response of linearly viscous fluids that are mechanically incompressible but thermally compressible. The present approach uses a nondimensionalization suggested by Chandrasekhar2 and utilizing the ratio of two characteristic velocities as a measure of smallness, systematically derives the Oberbeck-Boussinesq approximation as a third-order perturbation. In the present approach, the material is subjected to the constraint that the volume change is determined solely by the temperature change in the body and uses a novel approach in deriving the thermodynamical restrictions. Consequently, it is free from the additional assumptions usually added on in earlier works in order to obtain the correct equations.
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Téchené, Jean-Jacques. "Les aspects fondamentaux de l'admissibilité en approximation quadratique d'applications linéaires." Linear Algebra and its Applications 264 (October 1997): 389–419. http://dx.doi.org/10.1016/s0024-3795(96)00405-3.

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Barletta, Antonio, Michele Celli, and D. Andrew S. Rees. "On the Use and Misuse of the Oberbeck–Boussinesq Approximation." Physics 5, no. 1 (March 17, 2023): 298–309. http://dx.doi.org/10.3390/physics5010022.

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The Oberbeck–Boussinesq approximation is the most commonly employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the emergence of paradoxes or, at least, incorrect conclusions. In this paper, the basic features of the Oberbeck–Boussinesq approximation are briefly recalled and three simple examples where this theoretical scheme may be misused are provided. Such misuses of the approximation lead to erroneous conclusions that, in the examples presented in this note, entail violations of the principle of mass conservation. A discussion about the Oberbeck–Boussinesq approximation as an asymptotic theory obtained by letting the product of the thermal expansion coefficient and the reference temperature difference tend to zero is also presented.
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Gomes, Diogo A., and Claudia Valls. "Approximation of ill-posed boussinesq equations." Dynamical Systems 19, no. 4 (December 2004): 345–57. http://dx.doi.org/10.1080/1468936042000269587.

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Baron-Pertuz, Cristian-Fabian, Ana-Magnolia Marin-Ramirez, and Ruben-Dario Ortiz-Ortiz. "An approximation to the Boussinesq equations." International Journal of Mathematical Analysis 8 (2014): 2433–37. http://dx.doi.org/10.12988/ijma.2014.48274.

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PRUŠA, VÍT, and K. R. RAJAGOPAL. "ON MODELS FOR VISCOELASTIC MATERIALS THAT ARE MECHANICALLY INCOMPRESSIBLE AND THERMALLY COMPRESSIBLE OR EXPANSIBLE AND THEIR OBERBECK–BOUSSINESQ TYPE APPROXIMATIONS." Mathematical Models and Methods in Applied Sciences 23, no. 10 (July 12, 2013): 1761–94. http://dx.doi.org/10.1142/s0218202513500516.

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Viscoelastic fluid like materials that are mechanically incompressible but are compressible or expansible with respect to thermal stimuli are of interest in various applications ranging from geophysics and polymer processing to glass manufacturing. Here we develop a thermodynamical framework for the modeling of such materials. First we illustrate the basic ideas in the simpler case of a viscous fluid, and after that we use the notion of natural configuration and the concept of the maximization of the entropy production, and we develop a model for a Maxwell type viscoelastic fluid that is mechanically incompressible and thermally expansible or compressible. An important approximation in fluid mechanics that is frequently used in modeling buoyancy driven flows is the Oberbeck–Boussinesq approximation. Originally, the approximation was used for studying the flows of viscous fluids in thin layers subject to a small temperature gradient. However, the approximation has been used almost without any justification even for flows of non-Newtonian fluids induced by strong temperature gradients in thick layers. Having a full system of the governing equations for a Maxwell type viscoelastic mechanically incompressible and thermally expansible or compressible fluid, we investigate the validity of the Oberbeck–Boussinesq type approximation for flows of this type of fluids. It turns out that the Oberbeck–Boussinesq type approximation is in general not a good approximation, in particular if one considers "high Rayleigh number" flows. This indicates that the Oberbeck–Boussinesq type approximation should not be used routinely for all buoyancy driven flows, and its validity should be thoroughly examined before it is used as a mathematical model.
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Siddiqui, Perwez. "Density Modelling in Mixed Convection Flow in a Vertical Parallel Plate Channel." International Journal of Heat and Technology 39, no. 4 (August 31, 2021): 1294–304. http://dx.doi.org/10.18280/ijht.390428.

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In this paper, a novel way of modelling the density in buoyancy term of mixed convection flow problem is presented using equation of state and Boussinesq approximation without first-order approximation of density with respect to temperature. The presented density model is used to investigate the laminar mixed convection flow in a vertical parallel plate channel under symmetric constant wall heat flux. The results obtained are compared with the results obtained using first-order approximation of density with Boussinesq approximation, and also compared with the results obtained using variable thermophysical properties with negligible viscous dissipation. Investigation is performed on the basis of flow and thermal fields for Re=150 and 300, Ri=0.1 to 25. It is found that the presented density model produces relatively better results, which is able to describe the case of developing flow under constant heat flux condition that is not evident if Boussinesq approximation with first-order approximation of density is used. An appearance of recirculatory cells when reverse flow takes place is also witnessed in vertical channel flow with constant heat flux boundary condition which was not reported earlier.
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Grandi, Diego, and Arianna Passerini. "On the Oberbeck–Boussinesq approximation for gases." International Journal of Non-Linear Mechanics 134 (September 2021): 103738. http://dx.doi.org/10.1016/j.ijnonlinmec.2021.103738.

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Dissertations / Theses on the topic "Approximation de Boussinesq quadratique"

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Ferré, Alexis. "Etude CFD et expérimentale d'un stockage thermique de type thermocline." Electronic Thesis or Diss., Pau, 2024. http://www.theses.fr/2024PAUU3023.

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Le stockage d'énergie est essentiel à la transition énergétique car il permet de découpler la production de l'énergie de sa consommation. Le stockage de chaleur thermocline en eau, utilisé dans les réseaux de chaleur à moyenne ou basse température, repose sur la stratification thermique dans une cuve. Les performances de ce type de stockage sont fortement liées à la bonne stratification du fluide qui peut être perturbée par l'injection et le soutirage du liquide, des aspects peu explorés dans la littérature.L'objectif de cette thèse est de modéliser un tel stockage de manière fiable pour analyser la distribution du fluide. En effet, le but est de mieux appréhender les phénomènes physiques gouvernant la thermocline pendant les cycles de fonctionnement et d'accroître ses performances énergétiques par un design ou un pilotage amélioré. Pour ce faire, des études numériques utilisant la CFD (Computational Fluid Dynamics) ont été réalisées et comparées à des données expérimentales disponibles dans la littérature et obtenues via une nouvelle section d'essais.Dans un premier temps, un modèle CFD a été développé basé sur un cas expérimental existant de la littérature. Dans un stockage thermocline en eau, il y a bien souvent coexistence entre une région laminaire dans la cuve et turbulente à proximité des distributeurs. Cette coexistence est un enjeu majeur de la modélisation car la plupart des modèles de turbulence ne sont pas capables de représenter fiablement la transition d'un écoulement turbulent vers laminaire. Pour ces travaux, une méthode statistique RANS (Reynolds Average Numerical Simulation) est adoptée et le modèle k-omega-SST est sélectionnée car il permet de représenter les écoulements en proche paroi. Concernant la flottabilité, il existe deux méthodes pour considérer ses effets : utiliser une masse volumique variable dans l'ensemble des équations, ou constante sauf dans le terme de flottabilité . Cette dernière est connue sous le nom de l'approximation de Boussinesq mais n'est valable que sur une faible gamme de ΔT. La précision de l'approximation de Boussinesq a été remise en question et une approche au second ordre de ce modèle est employée. Celle-ci permet d'obtenir le même terme de flottabilité qu'un modèle à masse volumique variable mais avec un temps de calcul réduit de moitié. La comparaison avec des données expérimentales a permis de souligner l'impact de l'état initial en température (stockage stratifié ou homogène). Une étude exploratoire de l'impact d'une injection progressive selon une rampe en débit a montré son impact sur la réduction de l'épaisseur de la thermocline au moment de sa création.Dans une démarche de validation du modèle et de vérification des observations numériques, un nouveau dispositif expérimental a été conçu. Celui-ci mesure la température grâce à 300 thermocouples disposés dans la cuve et permet un contrôle précis des conditions opératoires. Des études en phase statiques pour évaluer les pertes thermiques ont été réalisées. Des études dynamiques ont permis de faire varier les paramètres opératoires pertinents : la vitesse de propagation axiale, l'écart de température, le dispositif de soutirage ou encore l'injection progressive. Pour ce système, les résultats montrent qu'il est possible d'obtenir une stratification à forte vitesse (> 2 mm/s) tant que le ΔT est suffisamment élevé.Enfin, l'écoulement dans la section d'essais a été étudié numériquement avec un modèle CFD actualisé. Les champs de variables ont montré que les résultats numériques et expérimentaux sont cohérents, en particulier lors de la formation de la thermocline. Toutefois, un excès de diffusion lors de la propagation du gradient thermique à faible débit est notable. Pour tous les essais réalisés les écarts expérimentaux et numériques ont été quantifiés: à l'exception des conditions critiques, l'écart sur l'épaisseur de thermocline est de ±50% et se situe entre 0 et -10% pour le taux de restitution
Energy storage is essential to the energy transition as it allows decoupling energy production from its consumption. Water-based thermocline heat storage, used in medium or low-temperature heating networks, relies on thermal stratification in a tank. The performance of this type of storage is strongly linked to the proper stratification of the fluid, which can be disrupted by the injection and extraction of the liquid, aspects that are scarcely explored in the literature.The objective of this thesis is to reliably model such storage to analyze the fluid distribution. The aim is to better understand the physical phenomena governing the thermocline during operating cycles and to enhance its energy performance through improved design or control. To achieve this, numerical studies using CFD (Computational Fluid Dynamics) were conducted and compared with experimental data available in the literature and obtained via a new experimental setup.Initially, a CFD model was developed based on an existing experimental case from the literature. In water thermocline storage, there is often coexistence between a laminar region in the tank and a turbulent region near the distributors. This coexistence is a major challenge in modeling because most turbulence models cannot reliably represent the transition from turbulent to laminar flow. For this work, a RANS (Reynolds Average Numerical Simulation) statistical method is adopted, and the k-omega-SST model is selected as it can represent near-wall flows. Regarding buoyancy, there are two methods to consider its effects: using a variable density in all equations or a constant density except in the buoyancy term. The latter is known as the Boussinesq approximation but is only valid over a narrow range of ΔT. The accuracy of the Boussinesq approximation has been questioned, and a second-order approach of this model is employed. This allows obtaining the same buoyancy term as a variable density model but with a calculation time reduced by half. Comparison with experimental data highlighted the impact of the initial temperature state (stratified or homogeneous storage). An exploratory study of the impact of progressive injection according to a flow ramp showed its effect on reducing the thermocline thickness at the time of its creation.As part of the model validation and verification of numerical observations, a new experimental setup was designed. It measures the temperature using 300 thermocouples placed in the tank and allows precise control of operating conditions. Static phase studies to evaluate thermal losses were conducted. Dynamic studies allowed varying relevant operating parameters: axial propagation speed, temperature difference, extraction device, and progressive injection. For this system, the results show that it is possible to obtain stratification at high speed (> 2 mm/s) as long as the ΔT is sufficiently high.Finally, the flow in the test section was numerically studied with an updated CFD model. The variable fields showed that the numerical and experimental results are consistent, especially during the formation of the thermocline. However, excessive diffusion during the propagation of the thermal gradient at low flow is notable. For all the tests carried out, the experimental and numerical discrepancies were quantified: except for critical conditions, the discrepancy in thermocline thickness is ±50% and ranges from 0 to -10% for the restitution rate
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McQuarrie, Shane Alexander. "Data Assimilation in the Boussinesq Approximation for Mantle Convection." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/6951.

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Many highly developed physical models poorly approximate actual physical systems due to natural random noise. For example, convection in the earth's mantle—a fundamental process for understanding the geochemical makeup of the earth's crust and the geologic history of the earth—exhibits chaotic behavior, so it is difficult to model accurately. In addition, it is impossible to directly measure temperature and fluid viscosity in the mantle, and any indirect measurements are not guaranteed to be highly accurate. Over the last 50 years, mathematicians have developed a rigorous framework for reconciling noisy observations with reasonable physical models, a technique called data assimilation. We apply data assimilation to the problem of mantle convection with the infinite-Prandtl Boussinesq approximation to the Navier-Stokes equations as the model, providing rigorous conditions that guarantee synchronization between the observational system and the model. We validate these rigorous results through numerical simulations powered by a flexible new Python package, Dedalus. This methodology, including the simulation and post-processing code, may be generalized to many other systems. The numerical simulations show that the rigorous synchronization conditions are not sharp; that is, synchronization may occur even when the conditions are not met. These simulations also cast some light on the true relationships between the system parameters that are required in order to achieve synchronization. To conclude, we conduct experiments for two closely related data assimilation problems to further demonstrate the limitations of the rigorous results and to test the flexibility of data assimilation for mantle-like systems.
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Haschke, Heike. "Splitting-Techniken zur spektralen Approximation der Navier-Stokes- und Boussinesq-Gleichungen." [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=96361083X.

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Rubio, Diana. "Distributed Parameter Control of Thermal Fluids." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30330.

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We consider the problem of controlling a thermal convection flow by feedback. The system is governed by the Boussinesq approximation of the coupled set of Navier-Stokes and heat equations. The control is applied through Dirichlet boundary conditions. We concentrate on a two-dimensional mode and use a semidiscrete Galerkin scheme for numerical computations. We construct both a linear control and a non-linear quadratic control and apply them to the full non-linear model. First, we test these controllers on a one-mode approximation. The convergence of the numerical scheme is analyzed. We also consider LQR control for a two-dimensional heat equation.
Ph. D.
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Hu, Weiwei. "Approximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systems." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/38664.

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In this thesis we present theoretical and numerical results for a feedback control problem defined by a thermal fluid. The problem is motivated by recent interest in designing and controlling energy efficient building systems. In particular, we show that it is possible to locally exponentially stabilize the nonlinear Boussinesq Equations by applying Neumann/Robin type boundary control on a bounded and connected domain. The feedback controller is obtained by solving a Linear Quadratic Regulator problem for the linearized Boussinesq equations. Applying classical results for semilinear equations where the linear term generates an analytic semigroup, we establish that this Riccati-based optimal boundary feedback control provides a local stabilizing controller for the full nonlinear Boussinesq equations. In addition, we present a finite element Galerkin approximation. Finally, we provide numerical results based on standard Taylor-Hood elements to illustrate the theory.
Ph. D.
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Schneider, Nicolas. "Vorticité et mélange dans les écoulements de Rayleigh-Taylor turbulents, en approximation anélastique et de Boussinesq." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066466/document.

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L'instabilité de Rayleigh-Taylor (IRT) est notamment rencontrée lors des expériences de Fusion par Confinement Inertiel, et son développement est un obstacle à la réussite de ces expériences. L'objet de cette thèse est d'étudier la croissance de l'IRT pour différents régimes de compressibilité, au moyen de simulations numériques directes réalisées à l'aide d'un code pseudo-spectral multidomaine de type Chebyshev-Fourier-Fourier.La méthode du développement asymptotique permet d'établir des modèles à bas nombre de Mach pour lesquels la contribution acoustique est éliminée. L'implantation dans le code de simulation du modèle anélastique, qui met en jeu des fluides stratifiés et capture les effets thermiques, est améliorée. Le modèle de Boussinesq est ajouté au code. La précision de la méthode numérique est étudiée pour différents découpages en sous-domaines. Plusieurs éléments de validation sont présentés, dont la comparaison avec une expérience.La première simulation présentée, réalisée avec le modèle de Boussinesq, s'intéresse à la croissance auto-semblable de l'IRT. Les lois d'échelle de la vorticité et de la dissipation sont dégagées. La structure de la turbulence et du mélange entre les deux fluides est discutée. Certaines propriétés de la turbulence homogène et isotrope sont retrouvées, mais on note la persistance d'anisotropie aux petites échelles. Les premières simulations 3D de l'IRT avec le modèle anélastique sont présentées. L'influence des effets de compressibilité sur les premières phases de la croissance est étudiée. En outre, une couche de mélange anélastique en faible stratification est analysée et présente des effets de compressibilité non négligeables
The Rayleigh-Taylor instability (RTI) is especially observed in inertial confinement fusion experiments, and its development prevents the success of these experiments. The purpose of this work is to study the growth of the RTI for different compressibility regimes by using a multidomain pseudospectral Chebyshev-Fourier-Fourier simulation code. The asymptotic expansion method allows to establish several low Mach number models which do not contains acoustics. The implantation of the anelastic model, which deals with stratified fluids and captures thermal effects, has been improved. Moreover, the Boussinesq model is added to the simulation code. The accuracy of the entire numerical method is studied, as a function of the subdomain separation, and several validation elements are shown, including a comparison with an experimental study. The first simulation to be analyzed is achieved with the Boussinesq model. We focus on the self-similarity of the RTI growth. The temporal scalings of vorticity and dissipation are displayed, and the structures of turbulence and mixing are discussed. Some properties of isotropic and homogeneous turbulence are observed, however some anisotropy remains at small scales. The first three-dimensional anelastic simulations are presented. The influence of compressibility effects on the first stages of the growth is studied. Finally, a developed anelastic mixing layer involving weakly stratified fluids is described and was found to display non-negligible compressibility effects
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Bérard, Bergery Blandine. "Approximation du temps local et intégration par régularisation." Thesis, Nancy 1, 2007. http://www.theses.fr/2007NAN10058/document.

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Cette thèse s'inscrit dans la théorie de l'intégration par régularisation de Russo et Vallois. La première partie est consacrée à l'approximation du temps local des semi-martingales continues. Si X est une diffusion réversible, on montre la convergence d'un premier schéma d'approximation vers le temps local de X, en probabilité uniformément sur les compacts. De ce premier schéma, on tire deux autres schémas d'approximation du temps local, l'un valable pour les semi-martingales continues, l'autre pour le mouvement Brownien standard. Dans le cas du mouvement Brownien, une vitesse de convergence dans L^2(Omega) et un résultat de convergence presque sûre sont établis. La deuxième partie de la thèse est consacrée à l'intégrale "forward" et à la variation quadratique généralisée, définies par des limites en probabilité de famille d'intégrales. Dans le cas Höldérien, la convergence presque sûre est établie. Enfin, on montre la convergence au second ordre pour une série de processus particuliers
The setting of this work is the integration by regularization of Russo and Vallois. The first part studies schemes of approximation of the local time of continuous semimartingales. If X is a reversible diffusion, the convergence of a first schema of approximation to the local time of X is proven, in probability uniformly on the compact sets. From this first schema, two other schemas of approximation for the local time are found. One converges in the semi-martingale case, the other in the Brownian case. Moreover, in the Brownian case, we estimate the rate of convergence in L^2(Omega) and a result of almost sure convergence is proven. The second part study the forward integral and the generalized quadratic variation, which have been defined by convergence of families of integrals, in probability uniformly on the compacts sets. In the case of Hölder processes, the almost sure convergence is proven. Finally, the second order convergence is studied in many cases
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Toqué, Nathalie. "Diffusion turbulente anisotrope dans les zones radiatives d'étoiles." Thèse, Paris 6, 2004. http://hdl.handle.net/1866/17334.

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Nguyen, Phuong Anh. "Contrôle optimal localisé sur des structures fines pour des équations paraboliques semilinéaires et le système de Boussinesq." Toulouse 3, 2000. http://www.theses.fr/2000TOU30195.

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Berard, Bergery Blandine. "Approximation du temps local et intégration par régularisation." Phd thesis, Université Henri Poincaré - Nancy I, 2007. http://tel.archives-ouvertes.fr/tel-00181777.

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Cette thèse s'inscrit dans la théorie de l'intégration par régularisation de Russo et Vallois. La première partie est consacrée à l'approximation du temps local des semi-martingales continues. On montre que, si $X$ est une diffusion réversible, alors $ \frac{1}{\epsilon}\int_0^t \left( \indi_{\{ y < X_{s+\epsilon}\}} - \indi_{\{ y < X_{s}\}} \right) \left( X_{s+\epsilon}-X_{s} \right)ds$ converge vers $L_t^y(X)$, en probabilité uniformément sur les compacts, quand $\epsilon \to 0$. De ce premier schéma, on tire deux autres schémas d'approximation du temps local, l'un valable pour les semi-martingales continues, l'autre pour le mouvement Brownien standard. Dans le cas du mouvement Brownien, une vitesse de convergence dans $L^2(\Omega)$ et un résultat de convergence presque sûre sont établis. La deuxième partie de la thèse est consacrée à l'intégrale "forward" et à la variation quadratique généralisée, définies par des limites en probabilité de famille d'intégrales. Dans le cas Höldérien, la convergence presque sûre est établie. Enfin, on montre la convergence au second ordre pour une série de processus particuliers.
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Books on the topic "Approximation de Boussinesq quadratique"

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Rubinstein, Robert. Renormalization group theory of Bolgiano scaling in Boussinesq turbulence. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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Merkle, Klaus. Einfluss gleich- und gegensinniger Drehrichtung der Verbrennungsluftstro me auf die Stabilisierung turbulenter Doppeldrall-Diffusionsflammen. Karlsruhe: Univ.-Verl. Karlsruhe, 2006.

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Book chapters on the topic "Approximation de Boussinesq quadratique"

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Herwig, Heinz. "Boussinesq-Approximation (Boussinesq approximation)." In Wärmeübertragung A-Z, 23–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-56940-1_6.

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Zeytounian, Radyadour. "The Boussinesq Approximation." In Asymptotic Modeling of Atmospheric Flows, 142–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-73800-5_8.

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Dewan, Anupam. "Models Based on Boussinesq Approximation." In Tackling Turbulent Flows in Engineering, 49–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14767-8_5.

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Feireisl, Eduard, and Maria E. Schonbek. "On the Oberbeck–Boussinesq Approximation on Unbounded Domains." In Nonlinear Partial Differential Equations, 131–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25361-4_7.

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Hinze, Michael, and Ulrich Matthes. "Optimal and Model Predictive Control of the Boussinesq Approximation." In International Series of Numerical Mathematics, 149–74. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-7721-2_7.

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Denisova, I. V., and V. A. Solonnikov. "Motion of Two Fluids in the Oberbeck-Boussinesq Approximation." In Motion of a Drop in an Incompressible Fluid, 205–32. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-70053-9_9.

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Straughan, Brian. "The Navier-Stokes Equations, the Boussinesq Approximation, and the Standard Bénard Problem." In The Energy Method, Stability, and Nonlinear Convection, 38–55. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-2194-2_3.

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Holm, Darryl D., Ruiao Hu, and Oliver D. Street. "On the Interactions Between Mean Flows and Inertial Gravity Waves in the WKB Approximation." In Mathematics of Planet Earth, 111–41. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-40094-0_5.

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AbstractWe derive a Wentzel–Kramers–Brillouin (WKB) closure of the generalised Lagrangian mean (GLM) theory by using a phase-averaged Hamilton variational principle for the Euler–Boussinesq (EB) equations. Following Gjaja and Holm 1996, we consider 3D inertial gravity waves (IGWs) in the EB approximation. The GLM closure for WKB IGWs expresses EB wave mean flow interaction (WMFI) as WKB wave motion boosted into the reference frame of the EB equations for the Lagrangian mean transport velocity. We provide both deterministic and stochastic closure models for GLM IGWs at leading order in 3D complex vector WKB wave asymptotics. This paper brings the Gjaja and Holm 1996 paper at leading order in wave amplitude asymptotics into an easily understood short form and proposes a stochastic generalisation of the WMFI equations for IGWs.
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Dorok, O., W. Grambow, and L. Tobiska. "Aspects of Finite Element Discretizations for Solving the Boussinesq Approximation of the Navier-Stokes Equations." In Numerical methods for the Navier-Stokes equations, 50–61. Wiesbaden: Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-663-14007-8_6.

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Naveen, P., and Ch RamReddy. "Soret and Viscous Dissipation Effects on MHD Flow Along an Inclined Channel: Nonlinear Boussinesq Approximation." In Numerical Heat Transfer and Fluid Flow, 267–74. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1903-7_31.

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Conference papers on the topic "Approximation de Boussinesq quadratique"

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Burns, John A., and Weiwei Hu. "Approximation methods for boundary control of the Boussinesq equations." In 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). IEEE, 2013. http://dx.doi.org/10.1109/cdc.2013.6759923.

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Xiao, Jianjun, John R. Travis, and Wolfgang Breitung. "Non-Boussinesq Integral Model for Horizontal Turbulent Strongly Buoyant Plane Jets." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48169.

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Horizontal buoyant jets are fundamental flow regimes for hydrogen safety analyses in the nuclear power plants. Integral model is an efficient, fast running engineering tool that can be used to obtain the jet trajectory, centerline dilution and other properties of the flow. In the published literature, most of the integral models that are used to predict the horizontal buoyant jet behavior employ the Boussinesq approximation, which limits the density range between the jets and the ambient. CorJet, a long researched, developed, and established commercial model, is such a Boussinesq model, and has proved to be accurate and reliable to predict the certain buoyant jet physics. In this study, Boussinesq and non-Boussinesq integral models with modified entrainment hypothesis were developed for modeling horizontal turbulent strongly buoyant plane jets. All the results and data where the Boussinesq model is valid will collapse to CorJet when they are properly normalized, which implies that the calculation is not sensitive to density variations in Boussinesq model. However, non-Boussinesq results will never collapse to CorJet analyses using the same normalized scaling, and the results are dependent on the density variation. The reason is that CorJet employs the Boussinesq approximation in which density variations are only important in the buoyancy term. For hydrogen safety analyses, the large density variation between hydrogen and the ambient, which is normally the mixture of air and steam, will make the Boussinesq approximation invalid, and the effect of the density variation on the inertial mass of the fluid can not neglected. This study highlights the assumption of the Boussinesq approximation as a limiting, simplified theory for strongly buoyant jets. A generalized scaling theory for horizontal strongly buoyant jet seems not to exist when the Boussinesq approximation is not applicable. This study also reveals that the density variation between jets and the ambient should be less than 10% to accurately model horizontal buoyant jets when the Boussinesq approximation is applied. Verification of this integral model is established with available data and comparisons over a large range of density variations with the CFD codes GASFLOW and Fluent. The model has proved to be an efficient engineering tool for predicting horizontal strongly buoyant plane jets.
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Wilson, Carlos Perez, and Serge Blancher. "ON THE BOUSSINESQ APPROXIMATION FOR THE POISEUILLE-RAYLEIGH-BENARD PROBLEM." In Proceedings of CHT-08 ICHMT International Symposium on Advances in Computational Heat Transfer. Connecticut: Begellhouse, 2008. http://dx.doi.org/10.1615/ichmt.2008.cht.1780.

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Gobbi, Maurício F., Andrew B. Kennedy, and James T. Kirby. "A Comparison of Higher Order Boussinesq and Local Polynomial Approximation Models." In 26th International Conference on Coastal Engineering. Reston, VA: American Society of Civil Engineers, 1999. http://dx.doi.org/10.1061/9780784404119.046.

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Mehdizadeh, A. M., M. R. Bazargan-Lari, A. Mansoori, and A. Mehdizadeh. "Two-Phase Flow Simulation of a Non-Boussinesq Density Current." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-37274.

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Boussinesq approximation was widely used in the previous studies to model dilute density or turbidity currents. This approximation was helping to simplify the governing equations and employing a single phase simulation of density currents. In contrast to the general approach of the previous researches who tried to avoid two-phase flow simulation, in this study the two-phase simulation of density current is performed to compare the solution based on the non-Boussinesq behaviour of the fluid with that assuming the Boussinesq approximation. The above goal has been achieved by employing the mixture model for the two-phase flow simulation. The geometry of study is based on a long shallow channel in which a high speed jet of salt-water entering the stilling fresh water via the sluice gate. Different turbulence models results have been compared with the experimental data in order to verify the best results. Also, results of two-phase simulation have been compared to those obtained by the Boussinesq approximation, results show that the two-phase simulation provides superior prediction compared to the conventional single phase flow simulation.
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Kamel, John K., and Samuel Paolucci. "Heat Transfer and Fluid Flow in a Furnace Using the Non-Boussinesq Approximation." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56466.

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Heat transfer and flow field distributions inside a furnace used for manufacturing carbon aircraft brakes are investigated by using non-Boussinesq equations. These equations, unlike their Boussinesq counterpart, enable us to account properly for the large variation of properties with temperature. Radiation between the furnace wall and the porous brake substrates is modelled by taking these surfaces as gray and diffuse, while the gas is considered to be a non-participating medium. A non-Darcian model is used for the flow in the porous brakes. We have implemented the equations within FIDAP, a commercial finite element code. The accuracy of the solution is validated by using well-established numerical solutions for laminar flows.
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Bhuyan, Shikha, and Dipankar Narayan Basu. "Numerical analysis of mixed convection flow using non-Boussinesq approximation lattice Boltzmann method." In Proceedings of the 25th National and 3rd International ISHMT-ASTFE Heat and Mass Transfer Conference (IHMTC-2019). Connecticut: Begellhouse, 2019. http://dx.doi.org/10.1615/ihmtc-2019.970.

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Pitz, Diogo B., John W. Chew, Olaf Marxen, and Nicholas J. Hills. "Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56486.

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A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretisation in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretise the governing equations, similarly to a finite element method, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretisation, and no subgrid modelling is included in the governing equations. Numerical results obtained for the rotor/stator cavity compare favourably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. For the buoyancy-driven flow, the energy equation is coupled to the momentum equations via the Boussinesq approximation, which has been implemented in the code considering two different formulations. Numerical predictions of the Nusselt number obtained using the traditional Boussinesq approximation are considerably higher than available experimental data. Much better agreement is obtained when the extended Boussinesq approximation is employed. It is concluded that the numerical method employed has considerable potential for further investigations of rotating cavity flows.
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Barhaghi, Darioush G., and Lars Davidson. "On the Validity of the Boussinesq Approximation in a Developing Mixed Convection Boundary Layer." In 2007 International Conference on Thermal Issues in Emerging Technologies: Theory and Application. IEEE, 2007. http://dx.doi.org/10.1109/theta.2007.363439.

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Zhou, Hongqiang, and Michelle H. Teng. "Higher-Order Modeling of Water Waves Generated by Submerged Moving Disturbances." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-80063.

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In this paper, a recently derived (Zhou, 2008) fully nonlinear and higher-order dispersive Boussinesq-type model for wave generation and propagation is presented. This new model is an extension of the wave propagation model by Gobbi and Kirby (1999) and Gobbi et al. (2000) to include the time-varying seabed bathymetry. The resulting new version retains the 4th-order approximation of the dispersion relation and the velocity distribution in the vertical direction, and extends the application to both water wave propagation and wave generation by seabed disturbances such as submarine landslides. The model equations are solved numerically through a higher-order finite difference scheme. To examine the validity of the new model and the improvement due to the higher-order extensions, numerical simulations of two wave generation cases are carried out based on the new 4th order model and an existing lower order Boussinesq model. The results show that the higher order model provides the more accurate prediction for the generated waves, especially those in the trailing region of shorter wavelengths where the traditional lower order Boussinesq model becomes much less accurate.
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