Relevant bibliographies by topics / Navier-Stokes equation

Academic literature on the topic 'Navier-Stokes equation'

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Published: 4 June 2021
Last updated: 1 August 2024

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Journal articles on the topic "Navier-Stokes equation"

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Ihsan, Hisyam, Syafruddin Side, and Muhammad Iqbal. "Solusi Persamaan Burgers Inviscid dengan Metode Pemisahan Variabel." Journal of Mathematics Computations and Statistics 4, no. 2 (October 28, 2021): 88. http://dx.doi.org/10.35580/jmathcos.v4i2.24442.

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Penelitian ini mengkaji tentang solusi persamaan Burgers Inviscid dengan metode pemisahan variabel. Tujuan dari penelitian ini adalah untuk mengetahui penyederhanaan sistem persamaan Navier-Stokes menjadi persamaan Burgers Inviscid, menemukan solusi persamaan Burgers Inviscid dengan metode pemisahan variabel, dan melakukan simulasi solusi persamaan dengan menggunakan software Maple18. Persamaan Burgers muncul sebagai penyederhanaan model yang rumit dari sistem persamaan Navier-Stokes. Persamaan Burgers adalah persamaan diferensial parsial hukum konservasi dan merupakan masalah hiperbolik, yaitu representasi nonlinier paling sederhana dari persamaan Navier-Stokes. Metode pemisahan variabel merupakan salah satu metode klasik yang efektif digunakan dalam menyelesaikan persamaan diferensial parsial dengan mengasumsikan untuk mendapatkan komponen x dan t. Kemudian akan dilakukan subtitusi pada persamaan diferensial, sehingga dengan cara ini akan didapatkan solusi persamaan diferensial parsial.Kata Kunci: Persamaan Burgers Inviscid, metode pemisahan variabel, persamaan Navier-StokesThis study examines the solution of Burgers Inviscid equation with variable separation method. The purpose of this study was to find out the simplification of the Navier-Stokes equation system into the Burgers Inviscid equation, find a solution to the Burgers Inviscid equation with the variable separation method, and simulate equation solutions using Maple18 software. The Burgers equation emerged as a complicated simplification of the Navier-Stokes equation system. The Burgers equation is a partial differential equation of conservation law and is a hyperbolic problem, i.e. the simplest nonlinear representation of the Navier-Stokes equation. The variable separation method is one of the classic methods that is effectively used in solving partial differential equations assuming to obtain the x and t components. Then there will be substitutions to differential equations, so that in this way there will be a partial differential equation solution.Keywords: Burgers Inviscid Equation, variable separation method, Navier-Stokes equations.
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Cruzeiro, Ana Bela. "Stochastic Approaches to Deterministic Fluid Dynamics: A Selective Review." Water 12, no. 3 (March 19, 2020): 864. http://dx.doi.org/10.3390/w12030864.

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We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the deterministic Navier–Stokes equation is regarded as a mean time derivative taken over stochastic Lagrangian paths and the equations of motion are critical points of an associated stochastic action functional involving the kinetic energy computed over random paths. Thus the deterministic Navier–Stokes equation is obtained via a variational principle. The pressure can be regarded as a Lagrange multiplier. The approach is based on Itô’s stochastic calculus. Different related probabilistic methods to study the Navier–Stokes equation are discussed. We also consider Navier–Stokes equations perturbed by random terms, which we derive by means of a variational principle.
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Rozumniuk, V. I. "About general solutions of Euler’s and Navier-Stokes equations." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2019): 190–93. http://dx.doi.org/10.17721/1812-5409.2019/1.44.

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Constructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler’s variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace’s and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler's and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.
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Youssef, Hairch, Abderrahmane Elmelouky, Mohamed Louzazni, Fouad Belhora, and Mohamed Monkade. "A numerical study of interface dynamics in fluid materials." Matériaux & Techniques 112, no. 4 (2024): 401. http://dx.doi.org/10.1051/mattech/2024018.

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This paper deals with the approximation of the dynamics of two fluids having non-matching densities and viscosities. The modeling involves the coupling of the Allen-Cahn equation with the time-dependent Navier-Stokes equations. The Allen-Cahn equation describes the evolution of a scalar order parameter that assumes two distinct values in different spatial regions. Conversely, the Navier-Stokes equations govern the movement of a fluid subjected to various forces like pressure, gravity, and viscosity. When the Allen-Cahn equation is coupled with the Navier-Stokes equations, it is typically done through a surface tension term. The surface tension term accounts for the energy required to create an interface between the two phases, and it is proportional to the curvature of the interface. The Navier-Stokes equations are modified to include this term, which leads to the formation of a dynamic interface between the two phases. The resulting system of equations is known as the two-phase Navier-Stokes/Allen-Cahn equations. In this paper, the authors propose a mathematical model that combines the Allen-Cahn model and the Navier-Stokes equations to simulate multiple fluid flows. The Allen-Cahn model is utilized to represent the diffuse interface between different fluids, while the Navier-Stokes equations are employed to describe the fluid dynamics. The Allen-Cahn-Navier-Stokes model has been employed to simulate the generation of bubbles in a liquid subjected to an acoustic field. The model successfully predicted the size of the bubbles and the frequency at which they formed. The numerical outcomes were validated against experimental data, and a favorable agreement was observed.
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Lee, Sunggeun, Shin-Kun Ryi, and Hankwon Lim. "Solutions of Navier-Stokes Equation with Coriolis Force." Advances in Mathematical Physics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/7042686.

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We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.
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Dlotko, Tomasz. "Navier–Stokes–Cahn–Hilliard system of equations." Journal of Mathematical Physics 63, no. 11 (November 1, 2022): 111511. http://dx.doi.org/10.1063/5.0097137.

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A growing interest in considering the “hybrid systems” of equations describing more complicated physical phenomena was observed throughout the last 10 years. We mean here, in particular, the so-called Navier–Stokes–Cahn–Hilliard equation, the Navier–Stokes–Poison equations, or the Cahn–Hilliard–Hele–Shaw equation. There are specific difficulties connected with considering such systems. Using the semigroup approach, we discuss here the existence-uniqueness of solutions to the Navier–Stokes–Cahn–Hilliard system, explaining, in particular, the limitation of maximal regularity of the local solutions imposed by the chosen boundary conditions.
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Ragusa, Maria Alessandra, and Veli B. Shakhmurov. "A Navier–Stokes-Type Problem with High-Order Elliptic Operator and Applications." Mathematics 8, no. 12 (December 21, 2020): 2256. http://dx.doi.org/10.3390/math8122256.

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The existence, uniqueness and uniformly Lp estimates for solutions of a high-order abstract Navier–Stokes problem on half space are derived. The equation involves an abstract operator in a Banach space E and small parameters. Since the Banach space E is arbitrary and A is a possible linear operator, by choosing spaces E and operators A, the existence, uniqueness and Lp estimates of solutions for numerous classes of Navier–Stokes type problems are obtained. In application, the existence, uniqueness and uniformly Lp estimates for the solution of the Wentzell–Robin-type mixed problem for the Navier–Stokes equation and mixed problem for degenerate Navier–Stokes equations are established.
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XU, KUN, and ZHAOLI GUO. "GENERALIZED GAS DYNAMIC EQUATIONS WITH MULTIPLE TRANSLATIONAL TEMPERATURES." Modern Physics Letters B 23, no. 03 (January 30, 2009): 237–40. http://dx.doi.org/10.1142/s0217984909018096.

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Based on a multiple stage BGK-type collision model and the Chapman–Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The new gas dynamic equations have the same structure as the Navier–Stokes equations, but the stress strain relationship in the Navier–Stokes equations is replaced by an algebraic equation with temperature differences. In the continuum flow regime, the new gas dynamic equations automatically recover the standard Navier–Stokes equations. The current gas dynamic equations are natural extension of the Navier–Stokes equations to the near continuum flow regime and can be used for near continuum flow study.
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Dou, Changsheng, and Zishu Zhao. "Analytical Solution to 1D Compressible Navier-Stokes Equations." Journal of Function Spaces 2021 (May 27, 2021): 1–6. http://dx.doi.org/10.1155/2021/6339203.

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There exist complex behavior of the solution to the 1D compressible Navier-Stokes equations in half space. We find an interesting phenomenon on the solution to 1D compressible isentropic Navier-Stokes equations with constant viscosity coefficient on x , t ∈ 0 , + ∞ × R + , that is, the solutions to the initial boundary value problem to 1D compressible Navier-Stokes equations in half space can be transformed to the solution to the Riccati differential equation under some suitable conditions.
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Wang, Wenjie, and Melkamu Teshome Ayana. "Simulation of J-Solution Solving Process of Navier–Stokes Equation." Mathematical Problems in Engineering 2021 (May 6, 2021): 1–8. http://dx.doi.org/10.1155/2021/9924948.

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To avoid grid degradation, the numerical analysis of the j-solution of the Navier–Stokes equation has been studied. The Navier–Stokes equations describe the motion of viscous fluid substances. On the basis of the advantages and disadvantages of the Navier–Stokes equations, the incompressible terms and the nonlinear terms are separated, and the original boundary conditions satisfying the j-solution of the Navier–Stokes equation are analyzed. Secondly, the development of a computational grid has been introduced; the turbulence model has also been described. The fluid form and the initial value of the j-solution of the Navier–Stokes equation are combined. The original boundary conditions are solved by a computer, and the nonlinear turbulence equations are derived, which control the fluid flow. The simulation of the fine grid is comprehended to analyze the research outcome. Simulation analysis is carried out to generate multiblock-structured grids with high quality. The j-solution on the grid points is the j-solution that can be used with a fewer number of meshes under the same conditions. The proposed work is easy to implement, and it consumes lesser memory. The results obtained are able to avoid mesh degradation skillfully, and the generated mesh exhibits the characteristics of smoothness, orthogonality, and controllability, which eventually improves the calculation accuracy.
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Dissertations / Theses on the topic "Navier-Stokes equation"

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Patni, Kavita. "Damped Navier-Stokes equation in 2D." Thesis, University of Surrey, 2016. http://epubs.surrey.ac.uk/809731/.

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The main object to study in this thesis is the so-called damped and driven Navier-Stokes equations. These equations differ from the classical Navier-Stokes system by the presence of the extra damping term which is greater than zero, which is often referred to as the Ekman damping term and models the bottom friction in two-dimensional oceanic models.
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Tryggeson, Henrik. "Analytical vortex solutions to Navier-Stokes equation." Doctoral thesis, Växjö universitet, Matematiska och systemtekniska institutionen, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1282.

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Fluid dynamics considers the physics of liquids and gases. This is a branch of classical physics and is totally based on Newton's laws of motion. Nevertheless, the equation of fluid motion, Navier-Stokes equation, becomes very complicated to solve even for very simple configurations. This thesis treats mainly analytical vortex solutions to Navier-Stokes equations. Vorticity is usually concentrated to smaller regions of the flow, sometimes isolated objects, called vortices. If one are able to describe vortex structures exactly, important information about the flow properties are obtained. Initially, the modeling of a conical vortex geometry is considered. The results are compared with wind-tunnel measurements, which have been analyzed in detail. The conical vortex is a very interesting phenomenaon for building engineers because it is responsible for very low pressures on buildings with flat roofs. Secondly, a suggested analytical solution to Navier-Stokes equation for internal flows is presented. This is based on physical argumentation concerning the vorticity production at solid boundaries. Also, to obtain the desired result, Navier-Stokes equation is reformulated and integrated. In addition, a model for required information of vorticity production at boundaries is proposed. The last part of the thesis concerns the examples of vortex models in 2-D and 3-D. In both cases, analysis of the Navier-Stokes equation, leads to the opportunity to construct linear solutions. The 2-D studies are, by the use of diffusive elementary vortices, describing experimentally observed vortex statistics and turbulent energy spectrums in stratified systems and in soapfilms. Finally, in the 3-D analysis, three examples of recent experimentally observed vortex objects are reproduced theoretically. First, coherent structures in a pipe flow is modeled. These vortex structures in the pipe are of interest since they appear for Re in the range where transition to turbulence is expected. The second example considers the motion in a viscous vortex ring. The model, with diffusive properties, describes the experimentally measured velocity field as well as the turbulent energy spectrum. Finally, a streched spiral vortex is analysed. A rather general vortex model that has many degrees of freedom is proposed, which also may be applied in other configurations.
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Vong, Seak Weng. "Two problems on the Navier-Stokes equations and the Boltzmann equation /." access full-text access abstract and table of contents, 2005. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b19885805a.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2005.
"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy" Includes bibliographical references (leaves 72-77)
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Hachicha, Imène. "Approximations hyperboliques des équations de Navier-Stokes." Thesis, Evry-Val d'Essonne, 2013. http://www.theses.fr/2013EVRY0015/document.

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Dans cette thèse, nous nous intéressons à deux approximations hyperboliques des équations de Navier-Stokes incompressibles en dimensions 2 et 3 d'espace. Dans un premier temps, on considère une perturbation hyperbolique de l'équation de la chaleur, introduite par Cattaneo en 1949, pour remédier au paradoxe de la propagation instantanée de cette équation. En 2004, Brenier, Natalini et Puel remarquent que la même perturbation, qui consiste à rajouter ε∂tt à l'équation, intervient en relaxant les équations d'Euler. En dimension 2, les auteurs montrent que, pour des sonnées régulières et sous certaines hypothèses de petitesse, la solution globale de la perturbation converge vers l'unique solution globale de (NS). En 2007, Paicu et Raugel améliorent les résultats de [BNP] en étendant la théorie à la dimension 3 et en prenant des données beaucoup moins régulières. Nous avons obtenu des résultats de convergence, avec données de régularité quasi-critique, qui complètent et prolongent ceux de [BNP] et [PR]. La seconde approximation que l'on considère est un nouveau modèle hyperbolique à vitesse de propagation finie. Ce modèle est obtenu en pénalisant la contrainte d'incompressibilité dans la perturbation de Cattaneo. Nous démontrons que les résultats d'existence globale et de convergence du précédent modèle sont encore vérifiés pour celui-ci
In this work, we are interested in two hyperbolic approximations of the 2D and 3D Navier-Stokes equations. The first model we consider comes from Cattaneo's hyperbolic perturbation of the heat equation to obtain a finite speed of propagation equation. Brenier, Natalini and Puel studied the same perturbation as a relaxed version of the 2D Euler equations and proved that the solution to this relaxation converges towards the solution to (NS) with smooth data, provided some smallness assumptions. Later, Paicu and Raugel improved their results, extending the theory to the 3D setting and requiring significantly less regular data. Following [BNP] and [PR], we prove global existence and convergence results with quasi-critical regularity assumptions on the initial data. In the second part, we introduce a new hyperbolic model with finite speed of propagation, obtained by penalizing the incompressibility constraint in Cattaneo's perturbation. We prove that the same global existence and convergence results hold for this model as well as for the first one
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Breckner, Hannelore. "Approximation and optimal control of the stochastic Navier-Stokes equation." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=961407050.

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Bible, Stewart Andrew. "STUDY OF THE "POOR MAN'S NAVIER-STOKES" EQUATION TURBULENCE MODEL." UKnowledge, 2003. http://uknowledge.uky.edu/gradschool_theses/310.

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The work presented here is part of an ongoing effort to develop a highly accurate and numerically efficient turbulence simulation technique. The paper consists of four main parts, viz., the general discussion of the procedure known as Additive Turbulent Decomposition, the derivation of the "synthetic velocity" subgrid-scale model of the high wavenumber turbulent fluctuations necessary for its implementation, the numerical investigation of this model and a priori tests of said models physical validity. Through these investigations we have demonstrated that this procedure, coupled with the use of the "Poor Mans Navier-Stokes" equation subgrid-scale model, has the potential to be a faster, more accurate replacement of currently popular turbulence simulation techniques since: 1. The procedure is consistent with the direct solution of the Navier-Stokes equations if the subgrid-scale model is valid, i.e, the equations to be solved are never filtered, only solutions. 2. Model parameter values are "set" by their relationships to N.S. physics found from their derivation from the N.S. equation and can be calculated "on the fly" with the use of a local high-pass filtering of grid-scale results. 3. Preliminary studies of the PMNS equation model herein have shown it to be a computationally inexpensive and a priori valid model in its ability to reproduce high wavenumber fluctuations seen in an experimental turbulent flow.
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Mosley, Nile Spencer. "Solutions to the Navier-Stokes equation set for spiral pipes." Thesis, Southampton Solent University, 1996. http://ssudl.solent.ac.uk/1269/.

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The research presented herein embodies three subject area specifically aimed at the investigation and application of the spiral geometry. These areas are: the derivation of a spiral coordinate system in E2; the formulation of a new metric suitable for spiral pipe structures; the numerical simulation of an incompressible viscous fluid flowing through spiral pipe structures. The spiral coordinate system is first derived and then proven admissible using differential geometry. Validation is achieved using the spiral coordinate system as an alternative transformation for mapping from Cartesian to Polar coordinates for the solution domain of the general wave equation from a square to a circular elastic membrane. Problems associated with curves that do not possess natural-parameterisation in terms of arc-length, and as such cannot use the standard form of the Frenet-Serrat formulae, are solved with the derivation of a generalized metric. This metric is presented and proven for use on an arbitrary shaped pipe of class 'n' and is especially suited for spiral pipe structures. The associated Christoffel symbols of the second kind are also derived and presented in association with the generalized metric for use with the tensorial form of the Navier-Stokes and continuity equations. Finally, the spiral coordinates system is extended into E3 for two types of pipe; the spiral conic and the spiral parabolic. The Continuity and Navier-Stokes equations are numerically solved for an incompressible viscous Newtonian fluid for these pipe structures with various inlet conditions and geometric constraints. A correlation is made with these solutions and solutions found for the helical pipe structure, the nearest equivalent to the spiral found in the open literature.
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Militaru, Mariana. "Sur les equations de navier-stokes deterministes et stochastiques et sur une equation elliptique." Clermont-Ferrand 2, 1997. http://www.theses.fr/1997CLF21922.

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Cette these, est constituee par trois problemes sur des conditions aux limites mixtes lies aux equations elliptiques et de navier-stokes. Dans la premiere partie, on montre l'existence d'une solution faible d'une equation de navier-stokes stochastique, lorsque la densite initiale s'annule. Apres avoir obtenu des estimations convenables sur des solutions approchees, on en deduit la convergence en loi dans un nouvel espace de probabilite. Par un passage a la limite elle obtient alors une solution verifiant une equation sous forme d'une esperance, donc une solution faible. Dans la seconde partie, on montre l'existence d'une solution de l'equation de navier stokes a densite variable en dimension 2. On a etudie le cas ou la vitesse est nulle sur une partie et ou sur une autre partie la vitesse tangentielle est nulle et la pression dynamique est fixee. On montre l'existence dans un espace de dimension finie et ensuite par passage a la limite, on a obtenu l'existence d'une solution dans un espace de sobolev. Dans la troisieme partie, on etablit l'existence et la regularite d'une solution d'un probleme elliptique dans un cylindre, avec des conditions aux limites mixtes : de type neumann ou la solution ne depend que de la hauteur sur la frontiere laterale. On a utilise une methode qui caracterise des espaces de sobolev, basee sur des estimations suivant des champs tangentielles a la frontiere.
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Lonsdale, G. "Multigrid methods for the solution of the Navier-Stokes equations." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379162.

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Zhou, Dong. "High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/295839.

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Mathematics
Ph.D.
Projection methods for the incompressible Navier-Stokes equations (NSE) are efficient, but introduce numerical boundary layers and have limited temporal accuracy due to their fractional step nature. The Pressure Poisson Equation (PPE) reformulations represent a class of methods that replace the incompressibility constraint by a Poisson equation for the pressure, with a suitable choice of the boundary condition so that the incompressibility is maintained. PPE reformulations of the NSE have important advantages: the pressure is no longer implicitly coupled to the velocity, thus can be directly recovered by solving a Poisson equation, and no numerical boundary layers are generated; arbitrary order time-stepping schemes can be used to achieve high order accuracy in time. In this thesis, we focus on numerical approaches of the PPE reformulations, in particular, the Shirokoff-Rosales (SR) PPE reformulation. Interestingly, the electric boundary conditions, i.e., the tangential and divergence boundary conditions, provided for the velocity in the SR PPE reformulation render classical nodal finite elements non-convergent. We propose two alternative methodologies, mixed finite element methods and meshfree finite differences, and demonstrate that these approaches allow for arbitrary order of accuracy both in space and in time.
Temple University--Theses
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Books on the topic "Navier-Stokes equation"

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Jacobs, P. A. Single-block Navier-Stokes integrator. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1991.

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Deissler, Robert G. On the nature of Navier-Stokes turbulence. Cleveland, Ohio: Lewis Research Center, 1989.

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Deissler, Robert G. On the nature of Navier-Stokes turbulence. [Washington, DC]: National Aeronautics and Space Administration, 1989.

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Deissler, Robert G. On the nature of Navier-Stokes turbulence. [Washington, DC]: National Aeronautics and Space Administration, 1989.

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Deissler, Robert G. On the nature of Navier-Stokes turbulence. [Washington, DC]: National Aeronautics and Space Administration, 1989.

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Andrea, Arnone, and United States. National Aeronautics and Space Administration., eds. Navier-Stokes turbine heat transfer predictions using two-equation turbulence. [Washington, DC: National Aeronautics and Space Administration, 1992.

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Andrea, Arnone, and United States. National Aeronautics and Space Administration., eds. Navier-Stokes turbine heat transfer predictions using two-equation turbulence. [Washington, DC: National Aeronautics and Space Administration, 1992.

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Andrea, Arnone, and United States. National Aeronautics and Space Administration., eds. Navier-Stokes turbine heat transfer predictions using two-equation turbulence. [Washington, DC: National Aeronautics and Space Administration, 1992.

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Andrea, Arnone, and United States. National Aeronautics and Space Administration., eds. Navier-Stokes turbine heat transfer predictions using two-equation turbulence. [Washington, DC: National Aeronautics and Space Administration, 1992.

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Demuren, A. O. Application of multi-grid methods for solving the Navier-Stokes equations. [Washington, DC]: National Aeronautics and Space Administration, 1990.

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Book chapters on the topic "Navier-Stokes equation"

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Debussche, Arnaud, Berenger Hug, and Etienne Mémin. "Modeling Under Location Uncertainty: A Convergent Large-Scale Representation of the Navier-Stokes Equations." In Mathematics of Planet Earth, 15–26. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_2.

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AbstractWe construct martingale solutions for the stochastic Navier-Stokes equations in the framework of the modelling under location uncertainty (LU). These solutions are pathwise and unique when the spatial dimension is 2D. We then prove that if the noise intensity goes to zero, these solutions converge, up to a subsequence in dimension 3, to a solution of the deterministic Navier-Stokes equation. This warrants that the LU Navier-Stokes equations can be interpreted as a large-scale model of the deterministic Navier-Stokes equation.
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Saramito, Pierre. "Navier–Stokes Equation." In Complex fluids, 1–62. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44362-1_1.

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Maciel, Walter J. "The Navier-Stokes Equation." In Undergraduate Lecture Notes in Physics, 87–96. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04328-9_7.

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Wang, C. Y. "The Navier–Stokes Equation." In Essential Analytic Laminar Flow, 1–9. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-36449-5_1.

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Kollmann, Wolfgang. "The Lewis-Kraichnan Equation for the Space-Time Functional." In Navier-Stokes Turbulence, 149–72. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-59578-3_10.

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Sengupta, Tapan K., and Swagata Bhaumik. "DNS of Navier–Stokes Equation." In DNS of Wall-Bounded Turbulent Flows, 17–120. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-0038-7_2.

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Schobeiri, Meinhard T. "Tensor Application, Navier–Stokes Equation." In Tensor Analysis for Engineers and Physicists - With Application to Continuum Mechanics, Turbulence, and Einstein’s Special and General Theory of Relativity, 119–31. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-35736-8_7.

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Goodair, Daniel. "Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes Equation with Stochastic Lie Transport." In Mathematics of Planet Earth, 87–107. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_7.

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AbstractWe present here a criterion to conclude that an abstract SPDE possesses a unique maximal strong solution, which we apply to a three dimensional Stochastic Navier-Stokes Equation. Motivated by the work of Kato and Lai we ask that there is a comparable result here in the stochastic case whilst facilitating a variety of noise structures such as additive, multiplicative and transport. In particular our criterion is designed to fit viscous fluid dynamics models with Stochastic Advection by Lie Transport (SALT) as introduced in Holm (Proc R Soc A: Math Phys Eng Sci 471(2176):20140963, 2015). Our application to the Incompressible Navier-Stokes equation matches the existence and uniqueness result of the deterministic theory. This short work summarises the results and announces two papers (Crisan et al., Existence and uniqueness of maximal strong solutions to nonlinear SPDEs with applications to viscous fluid models, in preparation; Crisan and Goodair, Analytical properties of a 3D stochastic Navier-Stokes equation, 2022, in preparation) which give the full details for the abstract well-posedness arguments and application to the Navier-Stokes Equation respectively.
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Tissot, Gilles, Étienne Mémin, and Quentin Jamet. "Stochastic Compressible Navier–Stokes Equations Under Location Uncertainty." In Mathematics of Planet Earth, 293–319. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-40094-0_14.

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AbstractThe aim of this paper is to provide a stochastic version under location uncertainty of the compressible Navier–Stokes equations. To that end, some clarifications of the stochastic Reynolds transport theorem are given when stochastic source terms are present in the right-hand side. We apply this conservation theorem to density, momentum and total energy in order to obtain a transport equation of the primitive variables, i.e. density, velocity and temperature. We show that performing low Mach and Boussinesq approximations to this more general set of equations allows us to recover the known incompressible stochastic Navier–Stokes equations and the stochastic Boussinesq equations, respectively. Finally, we provide some research directions of using this general set of equations in the perspective of relaxing the Boussinesq and hydrostatic assumptions for ocean modelling.
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Sun, Shu Ming, Ning Zhong, and Martin Ziegler. "On Computability of Navier-Stokes’ Equation." In Evolving Computability, 334–42. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20028-6_34.

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Conference papers on the topic "Navier-Stokes equation"

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Stańczy, Robert. "Stationary solutions of the generalized Smoluchowski–Poisson equation." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-31.

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Escher, Joachim, and Zhaoyang Yin. "Initial boundary value problems of the Degasperis-Procesi equation." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-10.

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Goncerzewicz, Jan. "On the initial-boundary value problems for a degenerate parabolic equation." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-13.

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Gramchev, Todor, and Grzegorz Łysik. "Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-14.

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Neustupa, Jiří, and Patrick Penel. "The Navier–Stokes equation with inhomogeneous boundary conditions based on vorticity." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-21.

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Schumacher, Katrin. "Solutions to the equation div u=f in weighted Sobolev spaces." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-26.

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Kubo, Takayuki, and Yoshihiro Shibata. "On the Stokes and Navier-Stokes flows in a perturbed half-space." In Regularity and Other Aspects of the Navier-Stokes Equation. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc70-0-10.

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Shibata, Yoshihiro, and Senjo Shimizu. "On the Stokes equation with Neumann boundary condition." In Regularity and Other Aspects of the Navier-Stokes Equation. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc70-0-15.

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Abels, Helmut. "Stokes equations in asymptotically flat layers." In Regularity and Other Aspects of the Navier-Stokes Equation. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc70-0-1.

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Zadrzyńska, Ewa. "On some free boundary problems for Navier-Stokes equations." In Regularity and Other Aspects of the Navier-Stokes Equation. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc70-0-17.

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Reports on the topic "Navier-Stokes equation"

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Newman, Christopher K. Exponential integrators for the incompressible Navier-Stokes equations. Office of Scientific and Technical Information (OSTI), July 2004. http://dx.doi.org/10.2172/975250.

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Kilic, M. S., G. B. Jacobs, J. S> Hesthaven, and G. Haller. Reduced Navier-Stokes Equations Near a Flow Boundary. Fort Belvoir, VA: Defense Technical Information Center, August 2005. http://dx.doi.org/10.21236/ada458888.

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Elman, Howard, and David Silvester. Fast Nonsymmetric Iterations and Preconditioning for Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, June 1994. http://dx.doi.org/10.21236/ada599710.

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Mikulevicius, R., and B. Rozovskii. Stochastic Navier-Stokes Equations. Propagation of Chaos and Statistical Moments. Fort Belvoir, VA: Defense Technical Information Center, January 2001. http://dx.doi.org/10.21236/ada413558.

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Luskin, Mitchell, and George R. Sell. Inertial Manifolds for Navier-Stokes Equations and Related Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, May 1991. http://dx.doi.org/10.21236/ada241805.

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Szymczak, William G. Viscous Split Algorithms for the Time Dependent Incompressible Navier Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, June 1989. http://dx.doi.org/10.21236/ada211592.

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McDonough, J. M., Y. Yang, and X. Zhong. Additive Turbulent Decomposition of the Incompressible and Compressible Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, January 1993. http://dx.doi.org/10.21236/ada277321.

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Evans, John A., and Thomas J. Hughes. Isogeometric Divergence-conforming B-splines for the Steady Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, April 2012. http://dx.doi.org/10.21236/ada560496.

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Evans, John A., and Thomas J. Hughes. Isogeometric Divergence-conforming B-splines for the Unsteady Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, April 2012. http://dx.doi.org/10.21236/ada560939.

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Gaitonde, Datta V., and Miguel R. Visbal. High-Order Schemes for Navier-Stokes Equations: Algorithm and Implementation Into FDL3DI. Fort Belvoir, VA: Defense Technical Information Center, August 1998. http://dx.doi.org/10.21236/ada364301.

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