Academic literature on the topic 'Conditions au bord de type Navier'
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Journal articles on the topic "Conditions au bord de type Navier"
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Siddique, MH, Abdus Samad, and Afzal Husain. "Combined effects of viscosity and surface roughness on electric submersible pump performance." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 231, no. 4 (April 3, 2017): 303–16. http://dx.doi.org/10.1177/0957650917702262.
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An electric submersible pump that lifts crude oil from well bore is a type of multi-stage centrifugal pump. The unexpected wellbore conditions like change in pumping fluid viscosity and sand production severely affect pump performance and eventually lead to breakdown. The present study proposes a numerical approach to understand the effects of fluid viscosity and surface roughness of the flow passages in an electric submersible pump at design and off-design conditions. A three-dimensional numerical analysis was carried out by solving Reynolds-averaged Navier–Stokes equations with shear stress transport turbulence model to characterize performance of the pump. The pumping fluids, i.e., water and crude oils of different viscosities were analyzed for different surface roughness ( Ks) values. The model predictions were compared with a theoretical one-dimensional model for the effect of viscosity and surface roughness. It was found that the disc-friction and the skin-friction losses are sensitive hydraulic losses of which the disc-friction loss increases with increase in viscosity, whereas skin-friction loss decreases with increase in surface roughness at high viscosity. The combined effect of viscosity and roughness showed a complicated behavior and eventually an improvement in pump performance at a higher surface roughness compared to a smoother and lowers surface roughness.
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Huijnen, V., L. M. T. Somers, R. S. G. Baert, L. P. H. de Goey, C. Olbricht, A. Sadiki, and J. Janicka. "Study of Turbulent Flow Structures of a Practical Steady Engine Head Flow Using Large-Eddy Simulations." Journal of Fluids Engineering 128, no. 6 (April 21, 2006): 1181–91. http://dx.doi.org/10.1115/1.2353259.
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The prediction performance of two computational fluid dynamics codes is compared to each other and to experimental data of a complex swirling and tumbling flow in a practical complex configuration. This configuration consists of a flow in a production-type heavy-duty diesel engine head with 130-mm cylinder bore. One unsteady Reynolds-averaged Navier-Stokes (URANS)-based simulation and two large-eddy simulations (LES) with different inflow conditions have been performed with the KIVA-3V code. Two LES with different resolutions have been performed with the FASTEST-3D code. The parallelization of the this code allows for a more resolved mesh compared to the KIVA-3V code. This kind of simulations gives a complete image of the phenomena that occur in such configurations, and therefore represents a valuable contribution to experimental data. The complex flow structures gives rise to an inhomogeneous turbulence distribution. Such inhomogeneous behavior of the turbulence is well captured by the LES, but naturally damped by the URANS simulation. In the LES, it is confirmed that the inflow conditions play a decisive role for all main flow features. When no particular treatment of the flow through the runners can be made, the best results are achieved by computing a large part of the upstream region, once performed with the FASTEST-3D code. If the inflow conditions are tuned, all main complex flow structures are also recovered by KIVA-3V. The application of upwinding schemes in both codes is in this respect not crucial.
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Amrouche, Cherif, and Nour El Houda Seloula. "On the Stokes equations with the Navier-type boundary conditions." Differential Equations & Applications, no. 4 (2011): 581–607. http://dx.doi.org/10.7153/dea-03-36.
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Hu, Weiwei, Yanzhen Wang, Jiahong Wu, Bei Xiao, and Jia Yuan. "Partially dissipative 2D Boussinesq equations with Navier type boundary conditions." Physica D: Nonlinear Phenomena 376-377 (August 2018): 39–48. http://dx.doi.org/10.1016/j.physd.2017.07.003.
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Ma, Lina, Rui Chen, Xiaofeng Yang, and Hui Zhang. "Numerical Approximations for Allen-Cahn Type Phase Field Model of Two-Phase Incompressible Fluids with Moving Contact Lines." Communications in Computational Physics 21, no. 3 (February 7, 2017): 867–89. http://dx.doi.org/10.4208/cicp.oa-2016-0008.
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AbstractIn this paper, we present some efficient numerical schemes to solve a two-phase hydrodynamics coupled phase field model with moving contact line boundary conditions. The model is a nonlinear coupling system, which consists the Navier-Stokes equations with the general Navier Boundary conditions or degenerated Navier Boundary conditions, and the Allen-Cahn type phase field equations with dynamical contact line boundary condition or static contact line boundary condition. The proposed schemes are linear and unconditionally energy stable, where the energy stabilities are proved rigorously. Various numerical tests are performed to show the accuracy and efficiency thereafter.
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Liu, An, Yuan Li, and Rong An. "Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions." Advances in Applied Mathematics and Mechanics 8, no. 6 (September 19, 2016): 932–52. http://dx.doi.org/10.4208/aamm.2014.m595.
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AbstractIn this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the H1 norm and the pressure in the L2 norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.
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Li, Yuan, and Rong An. "Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions." Abstract and Applied Analysis 2013 (2013): 1–17. http://dx.doi.org/10.1155/2013/125139.
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This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh sizeHin combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh sizeh. The error estimate obtained in this paper shows that ifH,h, andεcan be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.
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Kučera, Petr, and Jiří Neustupa. "OnL3-stability of strong solutions of the Navier–Stokes equations with the Navier-type boundary conditions." Journal of Mathematical Analysis and Applications 405, no. 2 (September 2013): 731–37. http://dx.doi.org/10.1016/j.jmaa.2013.04.037.
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Pineau, Benjamin, and Xinwei Yu. "On Prodi–Serrin type conditions for the 3D Navier–Stokes equations." Nonlinear Analysis 190 (January 2020): 111612. http://dx.doi.org/10.1016/j.na.2019.111612.
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Guo, Zhengguang, Petr Kučera, and Zdenek Skalak. "Navier–Stokes equations: regularity criteria in terms of the derivatives of several fundamental quantities along the streamlines—the case of a bounded domain." Nonlinearity 35, no. 11 (October 13, 2022): 5880–902. http://dx.doi.org/10.1088/1361-6544/ac8e4c.
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Abstract In this paper we deal with the conditional regularity of the weak solutions of the Navier–Stokes equations on a bounded domain endowed with Navier boundary conditions, Navier-type boundary conditions or Dirichlet boundary conditions. We prove the regularity criteria which are based on the directional derivatives of several fundamental quantities along the streamlines, namely the velocity magnitude, the kinetic energy, the pressure, the velocity field and the Bernoulli pressure. In striking contrast to the known criteria in which the mentioned quantities were differentiated along a fixed vector, our criteria are mostly optimal for the whole range of parameters and have a clear physical meaning.
Dissertations / Theses on the topic "Conditions au bord de type Navier"
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Wehbe, Elsy. "Magnetohydrodynamic of a non-newtonien fluid." Electronic Thesis or Diss., Pau, 2023. https://theses.hal.science/tel-04421152.
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La magnétohydrodynamique (MHD) est la discipline qui étudie le comportement des fluides conducteurs d'électricité lorsque leur mouvement est couplé au champ électromagnétique. Ici, nous étudions dans un domaine possiblement multi connexe dans 2D, l'existence des solutions pour un problème MHD couplant une équation de solution aqueuse de polymères avec l'équation de Maxwell de l'électromagnétisme. Pour résoudre notre problème, nous avons besoin de certaines estimations liées au problème associé de Stokes. L'une des difficultés réside dans la géométrie du domaine et le terme non linéaire d'ordre trois $(u cdot nabla)(u-alpha Delta u)$. D'autre part, il est démontré qu'il existe une régularité supplémentaire dans $W^{2,p}(O)$ pour le champ magnétiqueMagnetohydrodynamics (MHD) is the discipline studying the behavior of conductive fluids of electricity when their movement is coupled to the electromagnetic field. Here we study in $Omega$, a possibly multi-connected two-dimensional domain, the existence of solutions for an MHD coupling an equation of polymer aqueous solution with Maxwell equation of electromagnetic. To solve our problem we need some estimations related to the Stokes-associated problem. One of the difficulties is the geometry of the domain and the nonlinear term of third order $(u cdot nabla)(u-alpha Delta u)$. On the other hand, it is shown an additional regularity in $W^{2,p}(O)$ for the magnetic field
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Ghosh, Amrita. "Naviers-Stokes equations with Navier boundary condition." Thesis, Pau, 2018. http://www.theses.fr/2018PAUU3021/document.
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Le titre de ma thèse de doctorat est "Equations de Stokes et de Navier-Stokes avec la con- dition de Navier", où j’ai considéré l’écoulement d’un fluide newtonien visqueux, incompressible dans un domaine borné de R3. L’écoulement du fluide est décrit par les équations bien connues de Navier-Stokes, données par le système suivant ∂t − ∆u + (u • ∇)u + ∇π = 0, div u = 0 dans Ω × (0, T )u • n = 0, 2[(Du)n]τ + αuτ = 0 sur Γ × (0, T )u(0) = u0 dans Ω (0.1) dans un domaine borné Ω ⊂ R3 de frontière Γ, éventuellement non simplement connexe, de classe C1,1. La vitesse initiale u0 et le coefficient de friction α, scalaire, sont des fonctions don- nées. Les vecteurs unitaires normal extérieur et tangents à Γ sont notés n et τ respectivement et Du = 1 (∇u + ∇uT ) est le tenseur des déformations. Les fonctions u et π décrivent respective- ment les champs de vitesses et de pression du fluide dans Ω satisfaisant la condition aux limites (0.1.2).Cette condition aux limites, proposée par H. Navier en 1823, a été abondamment étudiée ces dernières années, qui pour de nombreuses raisons convient parfois mieux que la condition aux limites de Dirichlet sans glissement : elle offre plus de liberté et est susceptible de fournir une solution physiquement acceptable au moins pour certains des phénomènes paradoxaux résultant de la condition de non-glissement, comme par exemple le paradoxe de D’Alembert ou le paradoxe de non-collision.Ma thèse comporte trois parties. Dans la première, je cherche à savoir si le problème (0.1) est bien posé en théorie Lp, en particulier l’existence, l’unicité de solutions faibles, fortes dans W 1,p(Ω) et W 2,p(Ω) pour tout p ∈ (1, ∞), en considérant la régularité minimale du coefficient de friction α. Ici α est une fonction, pas simplement une constante qui reflète les diverses propriétés du fluide et/ou de la frontière, ce qui nous permet d’analyser le comportement de la solution par rapport au coefficient de frottement.Utilisant le fait que les solutions sont bornées indépendamment de α, on montre que la solution des équations de Navier-Stokes avec la condition de Navier converge fortement vers une solution des équations de Navier-Stokes avec la condition de Dirichlet, correspondant à la même donnée initiale dans l’espace d’énergie lorsque α → ∞. Des résultats similaires ont été obtenus pour le cas stationnaire.Le dernier chapitre concerne les estimations pour le problème de Robin pour le laplacien : l’opérateur elliptique de second ordre suivant, sous forme divergentielle dans un domaine bornéΩ ⊂ Rn de classe C1, avec la condition aux limites de Robin a été considéré div(A∇)u = divf + F dans Ω, ∂u+ αu = f n + g sur Γ.∂n (0.2) Les coefficients de la matrice symétrique A sont supposés appartenir à l’espace V MO(R3). Aussi α est une fonction appartenant à un certain espace Lq . En plus de prouver l’existence, l’unicité de solutions faibles et fortes, nous obtenons une borne sur u, uniforme par rapport à α pour α suffisamment large, en norme Lp. Pour plus de clarté, nous avons étudié séparément les deux cas: l’estimation intérieure et l’estimation au bordMy PhD thesis title is "Navier-Stokes equations with Navier boundary condition" where I have considered the motion of an incompressible, viscous, Newtonian fluid in a bounded do- main in R3. The fluid flow is described by the well-known Navier-Stokes equations, given by thefollowing system 1 )t − L1u + (u ⋅ ∇)u + ∇n = 0, div u = 01u ⋅ n = 0, 2[(IDu)n]r + aur = 0 in Q × (0, T )on Γ × (0, T ) (0.1) 11lu(0) = u0 in Qin a bounded domain Q ⊂ R3 with boundary Γ, possibly not connected, of class C1,1. The initialvelocity u0 and the (scalar) friction coefficient a are given functions. The unit outward normal and tangent vectors on Γ are denoted by n and r respectively and IDu = 1 (∇u + ∇uT ) is the rate of strain tensor. The functions u and n describe respectively the velocity2 and the pressure of a fluid in Q satisfying the boundary condition (0.1.2).This boundary condition, first proposed by H. Navier in 1823, has been studied extensively in recent years, among many reasons due to its contrast with the no-slip Dirichlet boundary condition: it offers more freedom and are likely to provide a physically acceptable solution at least to some of the paradoxical phenomenons, resulting from the no-slip condition, for example, D’Alembert’s paradox or no-collision paradox.My PhD work consists of three parts. primarily I have discussed the Lp -theory of well-posedness of the problem (0.1), in particular existence, uniqueness of weak and strong solutions in W 1,p (Q) and W 2,p (Q) for all p ∈ (1, ∞) considering minimal regularity on the friction coefficienta. Here a is a function, not merely a constant which reflects various properties of the fluid and/or of the boundary. Moreover, I have deduced estimates showing explicitly the dependence of u on a which enables us to analyze the behavior of the solution with respect to the friction coefficient.Using this fact that the solutions are bounded with respect to a, we have shown the solution of the Navier-Stokes equations with Navier boundary condition converges strongly to a solution of the Navier-Stokes equations with Dirichlet boundary condition corresponding to the sameinitial data in the energy space as a → ∞. The similar results have also been deduced for thestationary case.The last chapter is concerned with estimates for a Laplace-Robin problem: the following second order elliptic operator in divergence form in a bounded domain Q ⊂ Rn of class C1, withthe Robin boundary condition has been considered1div(A∇)u = divf + F in Q, 11 )u + u = f ⋅ n + g on Γ. (0.2) 2The coefficient matrix A is symmetric and belongs to V MO(R3). Also a is a function belonging to some Lq -space. Apart from proving existence, uniqueness of weak and strong solutions, we obtain the bound on u, uniform in a for a sufficiently large, in the Lp -norm. We have separately studied the two cases: the interior estimate and the boundary estimate to make the main idea clear in the simple set up
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Dhifaoui, Anis. "Équations de Stokes en domaine extérieur avec des conditions aux limites de type Navier." Thesis, Bourgogne Franche-Comté, 2020. http://www.theses.fr/2020UBFCD009.
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On s'intéresse aux équations stationnaires de Stokes posées dans un domaine extérieur tridimensionnel décrivant l'écoulement d'un fluide visqueux et incompressible autour d'obstacle supposé borné. La particularité ici réside dans les conditions au bord de l'obstacle que nous avons imposées. En effet, nous supposons que l'obstacle a une certaine rugosité et par conséquent, le fluide n'adhère pas au bord de l'obstacle mais, au contraire, il existe une friction dont on suppose décrite par les conditions aux limites de type Navier. Ces dernières modélisent d'une part l'imperméabilité de l'obstacle et d'autre part le fait que la composante tangentielle de la vitesse du fluide sur l'obstacle est proportionnelle au tenseur des déformations. Ce problème a été bien étudié lorsqu'il est posé dans un domaine borné. Les espaces de Sobolev classiques fournissent, dans ce cas, un cadre fonctionnel adéquat pour une étude complète. Cependant lorsque le domaine n'est pas borné, ces espaces ne sont plus adaptés car il est nécessaire de décrire le comportement à l'infini des solutions. On choisit alors de poser le problème dans des espaces de Sobolev avec des poids polynomiaux qui précisent la croissance ou la décroissance des fonctions à l'infini. Dans ce travail, nous commençons par effectuer une analyse hilbertienne du problème. Le point-clé ici est d'établir des inégalités de type Korn avec poids afin d'obtenir la coercivité de la forme bilinéaire associée à la formulation variationnelle. Nous continuons par démontrer des résultats d'existence, d'unicité et de régularité de solutions fortes et très faibles. Enfin, nous étudions l'extension de certains résultats en théorie L^pIn this manuscript, we study the three-dimensional stationary Stokes equations set in a exterior domain. The problem describes the flow of a viscous and incompressible fluid past a bounded obstacle. The distinctif feature here relies on the fact that the obstacle is assumed to a rough boundary. As a result, the fluid may slip on the boundary of the obstacle and, to take into account this property, we use the Navier boundary conditions. On the one hand, They model the impermeability of the obstacle, and on the other hand, the fact that the tangential component of the fluid velocity on the obstacle is proportional to the stress tensor. This problem has been well studied when set in a bounded domain. The standard Sobolev spaces provides, in this case, an adequate functional framework for a complete study. Since in our case, the domain is unbounded, these spaces are not adapted since it is necessary to describe the behaviour of the solutions to infinity. Therefore, we choose to set the problem in weighted Sobolev spaces where the weights describe the behaviour at infinity of the function (growth or decay).In this work, we first start by performing the mathematical analysis in the Hilbert setting. The key point here is to establish variant weighted Korn’s inequalities in order to get the coercivity of the bilinear form associated to the variational formulation. Next, we proved the existence, uniqueness of strong and very weak solutions. Finally, we study the extension of some of thses results to a weightedL^p-theory
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Al, Baba Hind. "Théorie des semi-groupes pour les équations de Stokes et de Navier-Stokes avec des conditions aux limites de type Navier." Thesis, Pau, 2015. http://www.theses.fr/2015PAUU3008/document.
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Cette thèse est consacrée à l'étude théorique mathématique des équations de Stokes et de Navier-Stokes dans un domaine borné de R^3 en utilisant la théorie des semi-groupes. Trois différents types de conditions seront considérés : des conditions aux limites de Navier, de type-Navier et des conditions qui dépendent de la pression. Ce manuscrit est composé de six chapitres. Tout d'abord nous commençons par un état de l'art sur les équations de Navier-Stokes. Ensuite nous démontrons l'analyticité du semi-groupe de Stokes avec chacune des conditions ci-dessus. Ceci permet de résoudre le problème d'évolution en utilisant la théorie des semi-groupes. Nous étudions également les puissances complexes et fractionnaires de l'opérateur de Stokes pour lesquelles nous démontrons certaines propriétés et estimations. Ces résultats seront utilisés dans la suite pour obtenir des estimations de type L^p-L^q pour le semi-groupe de Stokes, un résultat de régularité L^p-L^q maximale pour le problème de Stokes inhomogène et des résultats d'existence et d'unicité locale pour le problème non-linéaire. Après nous étudions le problème d'évolution de Stokes. Outre la régularité L^p-L^q maximale, nous démontrons l'existence des solutions faibles u∈L^q (0,T; W^(1,p) (Ω)), fortes u∈L^q (0,T; W^(2,p) (Ω)) et très faibles u∈L^q (0,T; L^p (Ω)) du problème de Stokes. On termine par l'étude du problème de Navier-Stokes avec chacune des conditions aux limites citées ci-dessus. Tout d'abord, en utilisant les estimations L^p-L^q on démontre l'existence d'une unique solution locale u qui vérifieu∈BC([0,T_0 ); L_(σ,τ)^p (Ω))∩L^q (0,T_0; L_(σ,τ)^r (Ω)), q,r>p, 2/q+3/r=3/p.De plus, pour une donnée initiale petite, on obtient l'existence globale des solutions. Ensuite en estimant le terme non-linéaire en fonction des puissances fractionnaires de l'opérateur de Stokes on démontre la régularité de la solutionThis thesis is devoted to the mathematical theoretical study of the Stokes and Navier-Stokes equations in a bounded domain of R^3 using the semi-group theory. Three different types of boundary conditions will be considered: Navier boundary conditions, Navier-type boundary conditions and boundary condition involving the pressure. This manuscript contains six chapters. We prove first the analyticity of the Stokes semi-group with each of the boundary conditions stated above. This allows us to solve the time dependent Stokes problem using the semi-group theory. We will study also the complex and fractional powers of the Stokes operator for which we prove some properties and estimations. These results will be used in the sequel to prove an estimate of type L^p-L^q for the Stokes semigroup, as well as the maximal L^p-L^q regularity for the inhomogeneous Stokes problem and an existence result for the non-linear problem. Next we study the time dependent Stokes problem, besides the maximal L^p-L^q regularity, we prove the existence of weak u∈L^q (0,T; W^(1,p) (Ω)), strong u∈L^q (0,T; W^(2,p) (Ω)) and very weak u∈L^q (0,T; L^p (Ω)) solutions to the Stokes problem. We end with the study of the Navier-Stokes problem. First using the L^p-L^q estimate for the Stokes semi-group we prove the existence of a unique local in time mild solution for the Navier-Stokes problem that verifies u∈BC([0,T_0 ); L_(σ,τ)^p (Ω))∩L^q (0,T_0; L_(σ,τ)^r (Ω)), q,r>p, 2/q+3/r=3/p.Furthermore, for some initial data the solution is global in time. Finally, by estimating the non-linear term as a function of the fractional powers of the Stokes operator we prove that the solution is regular
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Tomezyk, Jérôme. "Résolution numérique de quelques problèmes du type Helmholtz avec conditions au bord d'impédance ou des couches absorbantes (PML)." Thesis, Valenciennes, 2019. http://www.theses.fr/2019VALE0017/document.
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Dans cette thèse, nous étudions la convergence de méthode de type éléments finis pour les équations de Maxwell en régime harmonique avec condition au bord d'impédance et l'équation de Helmholtz avec une couche parfaitement absorbante(PML). On étudie en premier, la formulation régularisée de l'équation de Maxwell en régime harmonique avec condition au bord d'impédance (qui consiste à ajouter le term ∇ div à l'équation originale pour avoir un problème elliptique) et on garde la condition d'impédance comme une condition au bord essentielle. Pour des domaines à bord régulier, le caractère bien posé de cette formulation est bien connu mais cela n'est pas le cas pour des domaines polyédraux convexes. On commence alors le premier chapitre par la preuve du caractère bien posé dans le cas du polyèdre convexe, qui est basé sur le fait que l'espace variationnel est inclus dans H¹. Dans le but d'avoir des estimations explicites en le nombre d'onde k de ce problème, il est obligatoire d'avoir des résultats de stabilité explicites en ce nombre d'onde. C'est aussi proposé, pour quelques situations particulières, dans ce chapitre. Dans le second chapitre on décrit les singularités d'arêtes et de coins pour notre problème. On peut alors déduire la régularité de la solution du problème original, ainsi que de son adjoint. On a tous les ingrédients pour proposer une analyse de convergence explicite en k pour une méthode d'éléments finis avec éléments de Lagrange. Dans le troisième chapitre, on considère une méthode d'éléments finis hp non conforme pour un domaine à bord régulier. Pour obtenir des estimations explicites en k, on introduit un résultat de décomposition, qui sépare la solution du problème original (ou de son adjoint) en une partie régulière mais fortement oscillante et une partie moins régulière mais peu oscillante. Ce résultat permet de montrer des estimations explicites en k. Le dernier chapitre est dédié à l'équation de Helmholtz avec une PML. L'équation de Helmholtz dans l'espace entier est souvent utilisée pour modéliser la diffraction d'onde acoustique (en régime harmonique), avec la condition de radiation à l'infini de Sommerfeld. L'ajout d'une PML est une façon pour passer d'un domaine infini à un domaine fini, elle correspond à l'ajout d'une couche autour du domaine de calcul qui absorbe très vite toutes les ondes sortantes. On propose en premier un résultat de stabilité explicite en k. On propose alors deux schémas numériques, une méthode d'éléments finis hp et une méthode multi- échelle basée sur un sous-espace local de correction. Le résultat de stabilité est utilisé pour mettre en relation de choix des paramètres des méthodes numériques considérées avec k. Nous montrons aussi des estimations d'erreur a priori. A la fin de ces chapitres, des tests numériques sont proposés pour confirmer nos résultats théoriquesIn this thesis, we propose wavenumber explicit convergence analyses of some finite element methods for time-harmonic Maxwell's equations with impedance boundary condition and for the Helmholtz equation with Perfectly Matched Layer (PML). We first study the regularized formulation of time-harmonic Maxwell's equations with impedance boundary conditions (where we add a ∇ div-term to the original equation to have an elliptic problem) and keep the impedance boundary condition as an essential boundary condition. For a smooth domain, the wellposedness of this formulation is well-known. But the well-posedness for convex polyhedral domain has been not yet investigated. Hence, we start the first chapter with the proof of the well-posedness in this case, which is based on the fact that the variational space is embedded in H¹. In order to perform a wavenumber explicit error analysis of our problem, a wavenumber explicit stability estimate is mandatory. We then prove such an estimate for some particular configurations. In the second chapter, we describe the corner and edge singularities for such problem. Then we deduce the regularity of the solution of the original and the adjoint problem, thus we have all ingredients to propose a explicit wavenumber convergence analysis for h-FEM with Lagrange element. In the third chapter, we consider a non conforming hp-finite element approximation for domains with a smooth boundary. To perform a wavenumber explicit error analysis, we split the solution of the original problem (or its adjoint) into a regular but oscillating part and a rough component that behaves nicely for large frequencies. This result allows to prove convergence analysis for our FEM, again explicit in the wavenumber. The last chapter is dedicated to the Helmholtz equation with PML. The Helmholtz equation in full space is often used to model time harmonic acoustic scattering problems, with Sommerfeld radiation condition at infinity. Adding a PML is a way to reduce the infinite domain to a finite one. It corresponds to add an artificial absorbing layer surrounding a computational domain, in which scattered wave will decrease very quickly. We first propose a wavenumber explicit stability result for such problem. Then, we propose two numerical discretizations: an hp-FEM and a multiscale method based on local subspace correction. The stability result is used to relate the choice of the parameters in the numerical methods to the wavenumber. A priori error estimates are shown. At the end of each chapter, we perform numerical tests to confirm our theoritical results
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Casanova, Jean-Jérôme. "Analyse et contrôle de systèmes fluide-structure avec conditions limites sur la pression." Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30073/document.
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Le sujet de la thèse porte sur l'étude (existence, unicité, régularité) et le contrôle de problèmes fluide-structure possédant des conditions limites sur la pression. Le système étudié couple une partie fluide, décrite par les équations de Navier-Stokes incompressibles dans un domaine 2D et une partie structure, décrite par une équation 1D de poutre amortie située sur une partie du bord du domaine fluide. Dans le Chapitre 2, on étudie l'existence de solutions fortes pour ce modèle. Nous démontrons des résultats de régularité optimale pour le système de Stokes avec conditions de bord mixtes sur un domaine non régulier. Ces résultats sont ensuite utilisés pour prouver l'existence et l'unicité de solutions fortes, locales en temps, pour le système fluide-structure sans hypothèse de petitesse sur les données initiales. Le Chapitre 3 réutilise l'analyse précédente dans le cadre de solutions périodiques en temps. Nous développons un critère d'existence de solutions périodiques pour un problème parabolique abstrait. Ce critère est ensuite appliqué au système fluide-structure et nous obtenons l'existence de solutions strictes, périodiques et régulières en temps, pour des termes sources périodiques suffisamment petits. Le quatrième volet de la thèse porte sur la stabilisation du système fluide-structure au voisinage d'une solution périodique. Le système linéarisé sous-jacent est décrit à l'aide d'un opérateur A(t) dont le domaine dépend du temps. Nous démontrons l'existence d'un opérateur parabolique d'évolution pour ce système linéaire. Cet opérateur est ensuite utilisé, dans le cadre de la théorie de Floquet, pour étudier le comportement asymptotique du système. Nous adaptons la théorie existante pour des opérateurs à domaine constant au cas de domaine non constant. Nous obtenons la stabilisation exponentielle du système linéaire à l'aide d'un contrôle sur la frontière du domaine fluideIn this thesis we study the well-posedness (existence, uniqueness, regularity) and the control of fluid-structure system with boundary conditions involving the pressure. The fluid part of the system is described by the incompressible Navier- Stokes equations in a 2D rectangular type domain coupled with a 1D damped beam equation localised on a boundary part of the fluid domain. In Chapter 2 we investigate the existence of strong solutions for this model. We prove optimal regularity results for the Stokes system with mixed boundary conditions in non-regular domains. These results are then used to obtain the local-in-time existence and uniqueness of strong solutions for the fluid-structure system without smallness assumption on the initial data. Chapter 3 uses the previous analysis in the framework of periodic (in time) solutions. We develop a criteria for the existence of periodic solutions for an abstract parabolic system. This criteria is then used on the fluid- structure system to prove the existence of a periodic and regular in time strict solution, provided that the periodic source terms are small enough. In Chapter 4 we study the stabilisation of the fluid-structure system in a neighbourhood of a periodic solution. The underlying linear system involves an operator A(t) with a domain which depends on time. We prove the existence of a parabolic evolution operator for this linear system. This operator is then used to apply the Floquet theory and to describe the asymptotic behaviour of the system. We adapt the known results for an operator with constant domain to the case of operators with non constant domain. We obtain the exponential stabilisation of the linear system with control acting on a part of the boundary of the fluid domain
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Schmidt, Andreas [Verfasser], Reinhard [Akademischer Betreuer] Farwig, and Mads [Akademischer Betreuer] Kyed. "The Navier-Stokes Equations with Elastic Boundary and Boundary Conditions of Friction Type / Andreas Schmidt ; Reinhard Farwig, Mads Kyed." Darmstadt : Universitäts- und Landesbibliothek, 2021. http://d-nb.info/1236344863/34.
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Muzereau, Olivier. "Analyse des solutions du système des équations de Navier-Stokes avec des conditions aux limites de type vorticité pour les fluides barotropiques compressibles." Phd thesis, Université du Sud Toulon Var, 2009. http://tel.archives-ouvertes.fr/tel-00474984.
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Le travail présenté dans ce mémoire de thèse est consacré à l'analyse du système des équations de Navier-Stokes stationnaires pour les fluides barotropiques compressibles en géométrie bornée tridimensionnelle. La principale originalité tient au choix de conditions aux limites non classiques. Dans le cas inviscide, il s'agit alors des équations d'Euler, les conditions aux limites naturelles sont celles d'imperméabilité pour le champ des vitesses. Dans le cas visqueux, il faut introduire des conditions supplémentaires : en 2004 pour le modèle incompressible les professeurs J. Neustupa et P. Penel ont proposé de compléter les équations de Navier-Stokes par des conditions dites d'imperméabilité généralisée concernant également le champ de vorticité. Ils ont ainsi établi une théorie alternative à la théorie classique. Nous étendons cette théorie au modèle visqueux barotropique compressible. Nous présentons deux modèles approchés fondés sur un possible découplage en un problème de Stokes adéquat au choix des conditions aux limites et deux problèmes de Poisson avec conditions de Neumann. Cette approche met notamment en avant l'intérêt de la décomposition de Helmholtz, l'importance du théorème de Leray-Schauder pour démontrer l'existence de solutions, et le rôle essentiel d'une pression, dite pression effective. Quant aux passages à la limite, ils sont techniques et diffciles, mais désormais classiques. Nous nous sommes inspirés des travaux des écoles française (P.L. Lions) et tchèque (A. Novotny et I. Straskraba). Le second modèle approché fournit une solution à densité bornée. P.B. Mucha et M. Pokorny ont développé tout récemment la même analyse avec des conditions aux limites de Navier.
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Bhandari, Kuntal. "Boundary controllability of some coupled parabolic systems with Robin or Kirchhoff conditions." Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30063.
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Dans cette thèse, on étudie la contrôlabilité à zéro par le bord de quelques systèmes paraboliques linéaires couplés par des termes de couplage intérieur et/ou au bord. Le premier chapitre est une introduction à l'ensemble du manuscrit. Dans le deuxième chapitre, on rappelle les principaux concepts et résultats autour des notions de contrôlabilité qui seront utilisés dans la suite. Dans le troisième chapitre, on étudie principalement la contrôlabilité par le bord d'un système couplé 2x2 de type cascade avec des conditions au bord de Robin. En particulier, on prouve que les contrôles associés satisfont des bornes uniformes par rapport aux paramètres de Robin et convergent vers un contrôle de Dirichlet lorsque les paramètres de Robin tendent vers l'infini. Cette étude fournit une justification, dans le contexte du contrôle, de la méthode de pénalisation qui est couramment utilisée pour prendre en compte des données de Dirichlet peu régulières en pratique. Dans le quatrième et dernier chapitre, on étudie d'abord la contrôlabilité à zéro d'un système 2x2 en dimension 1 contenant des termes de couplage à la fois à l'intérieur et au bord du domaine. Plus précisément, on considère une condition de type Kirchhoff sur l'un des bords du domaine et un contrôle de Dirichlet sur l'autre bord, dans l'une ou l'autre des équations. En particulier, on montre que les propriétés de contrôle du système diffèrent selon que le contrôle agisse sur la première ou sur la seconde équation, et selon les valeurs du coefficient de couplage intérieur et du paramètre de Kirchhoff. On étudie ensuite un modèle 3x3 avec un ou deux contrôle(s) aux limites de Dirichlet à une extrémité et une condition de type Kirchhoff à l'autre extrémité ; ici la troisième équation est couplée (couplage intérieur) avec la première. Dans ce cas, on obtient ce qui suit : en considérant le contrôle sur la première équation, on a contrôlabilité conditionnelle dépendant des choix du coefficient de couplage intérieur et du paramètre de Kirchhoff, et en considérant le contrôle sur la deuxième équation, on obtient toujours une contrôlabilité positive. En revanche, considérer un contrôle sur la troisième équation conduit à un résultat de contrôlabilité négative. Dans cette situation, on a besoin de deux contrôles aux limites sur deux des trois équations pour retrouver la contrôlabilité. Enfin, on expose quelques études numériques basées sur l'approche pénalisée HUM pour illustrer les résultats théoriques, ainsi que pour tester d'autres exemplesIn this thesis, we study the boundary null-controllability of some linear parabolic systems coupled through interior and/or boundary. We begin by giving an overall introduction of the thesis in Chapter 1 and we discuss some essentials about the notion of parabolic controllability in the second chapter. In Chapter 3, we investigate the boundary null-controllability of some 2x2 coupled parabolic systems in the cascade form where the boundary conditions are of Robin type. This case is considered mainly in space dimension 1 and in the cylindrical geometry. We prove that the associated controls satisfy suitable uniform bounds with respect to the Robin parameters, which let us show that they converge towards a Dirichlet control when the Robin parameters go to infinity. This is a justification of the popular penalization method for dealing with Dirichlet boundary data in the framework of the controllability of coupled parabolic systems. Coming to the Chapter 4, we first discuss the boundary null-controllability of some 2x2 parabolic systems in 1-D that contains a linear interior coupling with real constant coefficient and a Kirchhoff-type condition through which the boundary coupling enters in the system. The control is exerted on a part of the boundary through a Dirichlet condition on either one of the two state components. We show that the controllability properties vary depending on which component the control is being applied; the choices of interior coupling coefficient and the Kirchhoff parameter play a crucial role to deduce positive or negative controllability results. Thereafter, we study a 3x3 model with one or two Dirichlet boundary control(s) at one end and a Kirchhoff-type boundary condition at the other; here the third equation is coupled (interior) through the first component. In this case we obtain the following: treating the control on the first component, we have conditional controllability depending on the choices of interior coupling coefficient and the Kirchhoff parameter, while considering a control on the second component always provides positive result. But in contrast, putting a control on the third entry yields a negative controllability result. In this situation, one must need two boundary controls on any two components to recover the controllability. Further in the thesis, we pursue some numerical studies based on the penalized Hilbert Uniqueness Method (HUM) to illustrate our theoretical results and test other examples in the framework of interior-boundary coupled systems
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Boyer, Franck. "Modélisation, Analyse et Approximation numérique en mécanique des fluides." Habilitation à diriger des recherches, Université de Provence - Aix-Marseille I, 2006. http://tel.archives-ouvertes.fr/tel-00104532.
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Ce travail est dédié à la mise en place de modèles d'écoulements de fluides complexes, à leur analyse théorique ainsi qu'au développement et à l'analyse de convergence de schémas numériques appropriés. Une première partie du travail concerne l'étude de modèles dits à interface diffuse pour les écoulements incompressibles multiphasiques. Après une étude assez précise du cadre diphasique, on propose la généralisation au cadre triphasique, ce qui nécessite d'introduire la notion importante de consistance des modèles. Des résultats numériques confirment la pertinence des modèles proposés. Ensuite, on s'intéresse au modèle plus classique de Navier-Stokes non-homogène incompressible pour lequel on établit le caractère bien posé du problème pour des conditions aux limites ouvertes non-linéaires en sortie d'un écoulement. Une brique essentielle de ce travail est l'étude détaillée du problème de traces pour l'équation de transport associée à un champ de vitesse peu régulier. Ce travail, dont l'intérêt dépasse le cadre applicatif décrit ci-dessus, fait l'objet d'un chapitre à part entière.
Dans une seconde partie, on s'intéresse à l'approximation numérique par des méthodes de volumes finis des solutions de problèmes elliptiques non-linéaires monotones (du type p-laplacien). Un premier chapitre décrit un certain nombre de résultats obtenus dans le contexte de maillages cartésiens. Un second chapitre est consacré à l'étude d'un cadre géométrique plus général par le biais de méthodes dites en dualité discrète. Une attention particulière est portée au cas où les coefficients du problème présentent des discontinuités spatiales, ce qui mène à des problèmes de transmission non-linéaire entre deux milieux.
Le mémoire s'achève par la description de quelques travaux connexes, d'une part sur une classe de schémas VF pour les équations elliptiques linéaires adaptés à des maillages non orthogonaux, et d'autre sur l'étude numérique de problèmes elliptiques couplés 2D/1D issus de la description asymptotique d'écoulements dans des milieux poreux fracturés.
Book chapters on the topic "Conditions au bord de type Navier"
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Rajagopal, K. R. "On Boundary Conditions for Fluids of the Differential Type." In Navier—Stokes Equations and Related Nonlinear Problems, 273–78. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1415-6_22.
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da Veiga, H. Beirão. "On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case." In Recent Developments of Mathematical Fluid Mechanics, 99–109. Basel: Springer Basel, 2016. http://dx.doi.org/10.1007/978-3-0348-0939-9_6.
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Amrouche, Chérif, and Elsy Wehbe. "Existence and Regularity of Solutions for the Magnetohydrodynamic Flow with Navier-Type Boundary Conditions in 2-D." In Fluids Under Control, 1–41. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27625-5_1.
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Chemin, Jean-Yves, Benoit Desjardins, Isabelle Gallagher, and Emmanuel Grenier. "Vertical Layers." In Mathematical Geophysics. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198571339.003.0018.
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From a physical point of view, as well as from a mathematical point of view, horizontal layers (Ekman layers) are now well understood. This is not the casefor vertical layers which are much more complicated, from a physical, analytical and mathematical point of view, and many open questions in all these directions remain open. Let us, in this section, consider a domain Ω with vertical boundaries. Namely, let Ωh be a domain of R2 and let Ω=Ωh × [0, 1]. This domain has two types of boundaries: • horizontal boundaries Ωh × {0} (bottom) and Ωh ×{1} (top) where Ekman layers are designed to enforce Dirichlet boundary conditions; • vertical boundaries ∂Ωh × [0, 1] where again a boundary layer is needed to ensure Dirichlet boundary conditions. These layers, however, are not of Ekman type, since r is now parallel to the boundary. Vertical layers are quite complicated. They in fact split into two sublayers: one of size E1/3 and another of size E1/4 where E =νε denotes the Ekman number. This was discovered and studied analytically by Stewartson and Proudman. Vertical layers can be easily observed in experiments (at least the E1/4 layer, the second one being too thin) but do not seem to be relevant in meteorology or oceanography, where near continents, effects of shores, density stratification, temperature, salinity, or simply topography are overwhelming and completely mistreated by rotating Navier–Stokes equations. In MHD, however, and in particular in the case of rotating concentric spheres, they are much more important. Numerically, they are easily observed, at large Ekman numbers E (small Ekman numbers being much more difficult to obtain). The aim of this section is to provide an introduction to the study of these layers, a study mainly open from a mathematical point of view. First we will derive the equation of the E1/3 layer. Second we will investigate the E1/4 layer and underline its similarity with Prandtl’s equations. In particular, we conjecture that E1/4 is always linearly and nonlinearly unstable. We will not prove this latter fact, which would require careful study of what happens at the corners of the domain, a widely open problem.
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Chalaev, Djamalutdin, and Nina Silnyagina. "DEVELOPMENT OF HIGH EFFICIENT SHELL-AND-TUBE HEAT EXCHANGERS BASED ON PROFILED TUBES." In Integration of traditional and innovation processes of development of modern science. Publishing House “Baltija Publishing”, 2020. http://dx.doi.org/10.30525/978-9934-26-021-6-42.
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The use of advanced heat transfer surfaces (corrugated tubes of various modifications) is an effective way to intensify the heat transfer and improve the hydraulic characteristics of tubular heat exchangers. The methods for evaluating the use of such surfaces as working elements in tubular heat exchangers have not been developed so far. The thermal and hydrodynamic processes occurring in the tubes with the developed surfaces were studied to evaluate the efficiency of heat exchange therein. Thin-walled corrugated flexible stainless steel tubes of various modifications were used in experimental studies. The researches were carried out on a laboratory stand, which was designed as a heat exchanger type "tube in tube" with a corrugated inner tube. The stand was equipped with sensors to measure the thermal hydraulic flow conditions. The comparative analysis of operation modes of the heat exchanger with a corrugated inner tube of various modifications and the heat exchanger with a smooth inner tube was performed according to the obtained data. Materials and methods. A convective component of the heat transfer coefficient of corrugated tube increased significantly at identical flow conditions comparing with a smooth tube. Increasing the heat transfer coefficient was in the range of 2.0 to 2.6, and increased with increasing Reynolds number. The increase in heat transfer of specified range outstripped the gain of hydraulic resistance caused by increase of the flow. Results and discussion. CFD model in the software ANSYS CFX 14.5 was adapted to estimate the effect of the tube geometry on the intensity of the heat transfer process. A two-dimensional axially symmetric computer model was used for the calculation. The model is based on Reynolds equation (Navier-Stokes equations for turbulent flow), the continuity equation and the energy equation supplemented by the conditions of uniqueness. SST-turbulence model was used for the solution of the equations. The problem was solved in the conjugate formulation, which allowed assessing the efficiency of heat exchange, depending on various parameters (coolant temperature, coolant velocity, pressure). The criteria dependences were obtained Nu = f (Re, Pr). Conclusions. The use a corrugated tube as a working element in tubular heat exchangers can improve the heat transfer coefficient of 2.0 - 2.6 times, with an increase in hydraulic resistance in the heat exchanger of 2 times (compared with the use of smooth tubes). The criteria dependences obtained on the basis of experimental studies and mathematical modeling allow developing a methodology for engineering calculations for the design of new efficient heat exchangers with corrugated tubes.
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Wang, Qing, Matthias Ihme, Yi-fan Chen, Vivian Yang, Fei Sha, and John Anderson. "Towards real-time predictions of large-scale wildfire scenarios using a fully coupled atmosphere-fire physical modelling framework." In Advances in Forest Fire Research 2022, 415–21. Imprensa da Universidade de Coimbra, 2022. http://dx.doi.org/10.14195/978-989-26-2298-9_67.
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With the changing climate, fire-exclusion, and expansion of wildland-urban interfaces, the frequency and severity of wildfires are expected to increase, putting substantial stress on fire management and authorities to mitigate the risk of wildfires. Improved physical models in conjunction with advanced high-performance computing resources offer new opportunities for operational use in examining potential fire-spread scenarios and planning. This work presents an open-source, high-fidelity modelling framework for simulating large-scale wildfire scenarios, taking into consideration atmospheric/fire coupling, complex terrain, and heterogeneous fuel loading. The framework is implemented using the TensorFlow programming environment on tensor processing units (TPUs). TPUs are a dedicated high-performance computing architecture to accelerate machine-learning applications and high-performance scientific computing. This framework solves the Favre-filtered reacting Navier-Stokes equations and the unclosed terms describing turbulence/chemistry interaction and turbulence transport are modelled using large-eddy simulation (LES) closures. Wildfire dynamics is described by a one-step solid-fuel pyrolysis/combustion model that is coupled to atmospheric flow dynamics using a Boussinesq-type approximation. A second-order finite-difference discretization is employed in a variable-density, low-Mach number formulation to discretize the governing equations, and an immersed-boundary method is adapted to represent complex terrain. In conjunction with the coupled atmosphere/fire model and physical models for turbulence/atmosphere/fire interaction, the resulting simulation framework enables high-resolution simulations (with spatial resolution below 2m) of large-scale fires that cover up to ~100,000 acres. Following the summary of validation results against a prescribed fire experiment to assess the overall accuracy at well-controlled conditions, we employ this coupled atmosphere/fire modelling framework to simulate a large-scale wildfire scenario that is representative of the 2017 California Tubb’s fire. To this end, we extract the terrain of the North Bay region of Calistoga and Santa Rosa, spanning an area of 20×20 km2, and consider a North-Eastern wind. The simulation results illustrate the rapid fire-spread dynamics and the coupling of the fire with the terrain and atmosphere. With relevance to operational and research applications that include parametric studies to examine effects of wind, fuel-density, other environmental factors, and fire-management strategies, we discuss the scalability and further extensions of the physical fidelity towards enabling real-time applications on TPU-compute architectures.
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Obodovych, Oleksandr, and Olesya Stepanova. "NUMERICAL SIMULATION OF THE PROCESSES OF HYDRODTNAMICS AND HEAT TRANSFER PROCESSES IN ROTOR-PULSATION APPARATUS." In Traditional and innovative approaches to scientific research: theory, methodology, practice. Publishing House “Baltija Publishing”, 2022. http://dx.doi.org/10.30525/978-9934-26-241-8-5.
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The development of energy-saving technologies that meet the modern requirements of product production is based on the development of new concepts, conducting comprehensive scientific research, and a detailed study of the essence of physical phenomena, which determines the possibility of purposeful management of the technological process and ensuring optimal conditions for its implementation. In the existing devices for the preparation of mixtures, grinding methods are used in hammer crushers and mills, which requires significant expenditure of mechanical (electrical) energy. Therefore, it is necessary to develop devices with a high degree of influence on the processed environment, which increases productivity and reduces energy consumption in technological processes. Such devices include rotary-pulsation devices, the principle of operation of which is based on the method of discrete-pulse energy input. The basis of this method is the multifactorial influence on the processed liquid homogeneous or heterogeneous environment, consisting of pressure pulsations, changes in the liquid flow rate, intense cavitation, developed turbulence, rigid cumulative impact, as well as high shear forces. The current task in this work is the study of the impact of discrete-pulse energy input mechanisms that take place in rotary-pulsation devices during the processing of heterogeneous media, as well as the development of new designs of devices of the specified type to obtain high-quality products. Therefore, the work is devoted to the development of a new design of the rotor-pulsation apparatus for the preparation of liquid mixtures, the principle of which is the use of a working chamber with a rotor and a stator, which have holes of different configurations. The purpose of the study is to conduct a comprehensive analysis of kinematic and dynamic characteristics and establish the features of discrete-pulse energy input during the dispersion of mixtures in a rotary-pulsation apparatus and to develop, on this basis, energy-saving technology and equipment for their preparation. Numerical modeling and experimental research of the processes of hydrodynamics and heat transfer in the mixture during its preparation were carried out. The working chamber of the device consists of a cylindrical rotor and stator containing round and rectangular perforated holes. The mathematical model includes the two- or three-dimensional Navier-Stokes equations, the κ-ε transport equation of the turbulence model, and the energy equation. Factors that affect the processes of deformation and destruction of dispersed particles in heterogeneous media processed in rotary-pulsation devices are pressure pulsations, as well as normal and tangential stress pulsations that occur in the flow when it passes through the working zone of the device. As a result of numerical studies, the fields of velocities, pressures and temperatures of the studied media were found, and the most optimal geometric characteristics of the working chamber of the rotary-pulsation apparatus were determined. Based on the obtained results of numerical simulation, the designs of the rotor-pulsation apparatus will be selected, which will be used for the production of industrial research samples of this device.
Conference papers on the topic "Conditions au bord de type Navier"
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Chemetov, Nikolai V. "The Rigid Body Motion in Cosserat´s Fluid with Navier´s Slip Boundary Conditions." In Topical Problems of Fluid Mechanics 2022. Institute of Thermomechanics of the Czech Academy of Sciences, 2022. http://dx.doi.org/10.14311/tpfm.2022.003.
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The aim of this article is to give a brief presentation of recent results related to the body-fluid interaction problem. The motion is described by a system of coupled differential equations: Newton’s second law and Navier Stokes type equations. We shall formulate the global solvability result of weak solution of the problem, when the slippage is allowed at the boundaries of the rigid body and of the bounded domain, occupied by the fluid.
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Liu, Huaxing, Soon Keat Tan, Jing Li, and Xikun Wang. "Three Dimensional Simulation of Bore Flow Using SPH." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-21090.
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Tidal bore is a fascinating and powerful hydraulic phenomenon. In this paper, the tidal bore’s process is studied using 3D Smooth Particle Hydrodynamic (SPH) model. The Lagrangian nature of SPH suits well to the modeling of the complex fluid flow phenomenon. In the SPH method, the Navier-Stokes equations are discretized with fluid particles in the Lagrangine sense. Boundary conditions, including both no slip wall and bottom wall, are implemented using dynamic boundary particles. Using SPH, the bore’s generation together with its traverse along the channel are presented, including the description of flow field and bore’s configuration. Different types of bores’ behavior are investigated. It is observed that there is a splash of water surge up the wall and the front of the bore becomes a breaker wave when the initial water column travels at high speed. The velocity field and bore heights at different locations are visualized and discussed as well.
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Rhee, Shin Hyung. "A Validation Study for Tank Sloshing Using a Navier-Stokes Solver." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51083.
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The present study is concerned with the liquid tank sloshing at low filling level conditions. The volume of fluid method implemented in a Navier-Stokes computational fluid dynamics code is employed to handle the free-surface flow of liquid sloshing. A geometric reconstruction scheme for the interface representation is employed to ensure sharpness at the free-surface. The governing equations are discretized by second order accurate schemes on unstructured grids. Several different computational approaches are verified and numerical uncertainties are assessed. The computational results are validated against existing experimental data, showing good agreement. The capability is demonstrated for a generic membrane type LNG carrier tank with a simplified pump tower inside. The validation results suggest that the present computational approach is both easy to apply and accurate enough for more realistic problems.
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Zachariadis, Alexios, and Cesare A. Hall. "Application of a Navier-Stokes Solver to the Study of Open Rotor Aerodynamics." In ASME Turbo Expo 2009: Power for Land, Sea, and Air. ASMEDC, 2009. http://dx.doi.org/10.1115/gt2009-59332.
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This paper establishes a proven computational approach for open rotor configurations that can be used as a basis for further studies involving open rotor aerodynamics and design. Many of the difficulties encountered in the application of computational fluid dynamics to an open rotor engine arise due to the removal of the casing that is present in conventional aeroengine turbomachinery. In this work, an advanced three-dimensional Navier-Stokes solver is applied to the open rotor. The approach needed to accurately capture the aerodynamics is investigated with particular attention to the mesh configuration and the specification of boundary conditions. A new three-step meshing strategy for generating the mesh and the most suitable type of far-field boundary condition are discussed. A control volume analysis approach is proposed for post-processing the numerical results for rotor performance. The capabilities of the solver and the applied methodology are demonstrated at both cruise and take-off operating conditions. The comparison of computational results with experimental measurements shows good agreement for both data trend and magnitudes.
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Yeuan, J. J., A. Hamed, and W. Tabakoff. "Navier-Stokes Computations for Turbulent Flow Predictions in Transonic Turbine Cascade Using a Zonal Approach." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-240.
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Numerical results are presented for viscous flow through a transonic turbine cascade using different turbulence models and H-type grids. The explicit Navier-Stokes solver used in the solution was developed with an option of conservative zonal approach for interpolation across the periodic boundaries with minimum numerical errors. This approach allows the use of a grid that is more orthogonal and less skewed which leads to higher accuracy in the prediction of turbine blade performance. The results obtained with an algebraic and two equation turbulence models, and with two types of H grids are compared at two different flow conditions.
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Tuncer, Ismail H., Stefan Weber, and Wolfgang Sanz. "Investigation of Periodic Boundary Conditions in Multi-Passage Cascade Flows Using Overset Grids." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-011.
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A Navier-Stokes solution method with overset grids is applied to unsteady multi-passage cascade flows, and the unsteady blade loadings are compared against the single passage solutions with the direct store interblade boundary condition. In the overset grid solutions, the multi-passage domain is discretized with O-type grids around each blade and a rectangular background grid. Blade grids are allowed to move in time relative to the background grid as prescribed by the oscillatory plunging motion. The overset grid method uses a simple, robust numerical algorithm to localize moving intergrid boundary points and to interpolate solution variables across grids. Computational results are presented for two and four passage, subsonic and transonic flows through a turbine and a compressor cascade. The overset grid solutions over the multi-passage periodic domains agree well with the single passage solutions and the experimental data. It is concluded that the time linearization error introduced by the direct store approach is negligible in the range of flow conditions studied.
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Dejean, F., C. Vassilopoulos, G. Slmandirakis, K. C. Giannakoglou, and K. D. Papailiou. "Analysis of Transonic Turbomachinery Flows Using a 2-D Explicit Low-Reynolds k-ε Navier-Stokes Solver." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-063.
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An explicit, time-marching fractional-step solver for the calculation of the two-dimensional compressible Navier-Stokes equations is presented. The advantage of using a fractional-step analysis is its simplicity and the fact that greater time-steps are allowed, since the stability criterion is less strict compared to other explicit solvers. Turbulence is modeled through a low-Reynolds k-ε model, for which a novel artificial viscosity scheme is implemented, ensuring a smooth ε-distribution close to solid walls. The method is used in order to numerically investigate the flow field in three different cascades, namely a highly loaded transonic linear turbine guide vane cascade in six different flow conditions, a transonic steam turbine cascade in two different flow conditions and a low supersonic compressor cascade. Calculations are performed using both H- and C-type grids.
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Azadian-Kharanjani, Zohreh, Amir H. Nikseresht, and Harry B. Bingham. "A Numerical Investigation of Wedge Angle Effects on a Plunger Type Wave Maker With a Constant Submerged Volume." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-77380.
Full textAbstract:
The effect of wedge angle at a constant submerged volume for a plunger type wave maker on the wave height, wave amplitude ratio and the quality of generated wave is studied numerically for a range of linear wave conditions in this research. The commercial ANSYS-FLUENT finite volume code is used to solve the Navier-Stokes equations using dynamic meshes and a Volume of Fluid (VOF) scheme is used to capture the air-water interface. A second order upwind numerical scheme is used to discretize the convective terms of the momentum equations and the standard SIMPLE algorithm is used for coupling the pressure and velocity based equations. At first the plunger-type wedge shaped wave-maker of Wang is considered numerically for the conditions used in his experiments, over a range of linear wave conditions (H/λ less than or equal to 0.03). After validating the numerical method, the effect of plunger wedge angle on the quality of the generated waves and on the power which is needed to run the wave maker are investigated. From these results, we conclude that the quality of the generated waves reduces with increasing wedge angle, when the submerged volume is fixed.
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Yadav, A., R. Calhoun, P. E. Phelan, A. K. Vuppu, A. A. Garcia, and M. A. Hayes. "Simulation of Magneto-Rheological Fluids Using Lattice Boltzmann Method." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60301.
Full textAbstract:
Lattice Boltzmann (LB) simulations of Magneto-rheological fluids under a rotating magnetic field are presented in this paper. The LB method gives a complete solution of Navier-Stokes equation based on the Boltzmann transport equation. A relatively good agreement of normalized number of aggregated particles in experiments and simulations is found. Results pertaining to variation of chain length vs. Mason number are also shown. A complete analysis and comparison of forces on the particles found from LB simulations and from simple Particle dynamics (PD) type approach is also shown. Another aim of this study was to determine under what conditions do we need to solve the complete Navier-Stokes equations and under what conditions a simplistic but very fast simulation method like particle dynamics will work for Magneto-rheological fluids.
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Raif, Markus, Jürgen F. Mayer, and Heinz Stetter. "Comparison of a TVD-Upwind Scheme and a Central Difference Scheme for Navier-Stokes Turbine Stage Flow Calculation." In ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-031.
Full textAbstract:
The differences of two distinct numerical schemes implemented in one code called ITSM3D are presented for a turbine stage test case. Thus both schemes are used with exactly the same computational infrastructure, e. g, same grids, boundary conditions, acceleration strategies, time-stepping, turbulence model etc. The two methods are based on an explicit Runge-Kutta-type finite volume scheme expressed in cylindrical coordinates and have been developed at the Institut für Thermische Strömungsmaschinen und Maschinenlaboratorium of the University of Stuttgart. One scheme is a node centered 3rd order TVD scheme according to Osher and the other belongs to the cell vertex central difference type with the concept of artificial viscosity. The model of Baldwin-Lomax is used in order to simulate turbulent effects. Non-reflective boundary conditions are taken at stator inlet and rotor outlet to avoid non-physical reflections. A multigrid technique in combination with implicit residual smoothing and local time-stepping is employed to accelerate the computation. The test case for this comparison is the last stage of a low-pressure turbine. The computational results obtained are discussed and compared to each other as well as to experimental data. They are presented as pressure and Mach number isoline contours and diagrams of circumferential averaged quantities at inlet and outlet planes of stator and rotor versus radial position.