A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection PDF Download

Author: Ann S. Almgren
Publisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 16

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Author:
Publisher: Springer Science & Business Media
ISBN: 3663111717
Category : Technology & Engineering
Languages : en
Pages : 302

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Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. '... this book should be mandatory reading for applied mathematicians specializing in computational fluid dynamics.' J.-L.Guermond. Mathematical Reviews, Ann Arbor

Author: Friedrich-Karl Hebeker
Publisher: Springer-Verlag
ISBN: 3663140075
Category : Technology & Engineering
Languages : de
Pages : 328

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Author: John G. Heywood
Publisher: Springer
ISBN: 3540474986
Category : Science
Languages : en
Pages : 329

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V.A. Solonnikov, A. Tani: Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid.- W. Borchers, T. Miyakawa:On some coercive estimates for the Stokes problem in unbounded domains.- R. Farwig, H. Sohr: An approach to resolvent estimates for the Stokes equations in L(q)-spaces.- R. Rannacher: On Chorin's projection method for the incompressible Navier-Stokes equations.- E. S}li, A. Ware: Analysis of the spectral Lagrange-Galerkin method for the Navier-Stokes equations.- G. Grubb: Initial value problems for the Navier-Stokes equations with Neumann conditions.- B.J. Schmitt, W. v.Wahl: Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the Boussinesq-equations.- O. Walsh: Eddy solutions of the Navier-Stokesequations.- W. Xie: On a three-norm inequality for the Stokes operator in nonsmooth domains.

Author: L. Quartapelle
Publisher: Birkhäuser
ISBN: 3034885792
Category : Science
Languages : en
Pages : 296

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This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.

Author: Roger Temam
Publisher: Elsevier
ISBN: 1483256855
Category : Mathematics
Languages : en
Pages : 539

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Navier-Stokes Equations: Theory and Numerical Analysis focuses on the processes, methodologies, principles, and approaches involved in Navier-Stokes equations, computational fluid dynamics (CFD), and mathematical analysis to which CFD is grounded. The publication first takes a look at steady-state Stokes equations and steady-state Navier-Stokes equations. Topics include bifurcation theory and non-uniqueness results, discrete inequalities and compactness theorems, existence and uniqueness theorems, discretization of Stokes equations, existence and uniqueness for the Stokes equations, and function spaces. The text then examines the evolution of Navier-Stokes equations, including linear case, compactness theorems, alternate proof of existence by semi-discretization, and discretization of the Navier-Stokes equations. The book ponders on the approximation of the Navier-Stokes equations by the projection and compressibility methods; properties of the curl operator and application to the steady-state Navier-Stokes equations; and implementation of non-conforming linear finite elements. The publication is a valuable reference for researchers interested in the theory and numerical analysis of Navier-Stokes equations.

Author: Vorleak Yek
Publisher:
ISBN: 9780438258624
Category : Fluid dynamics
Languages : en
Pages : 76

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Abstract: The motion of a viscous fluid flow is described by the well-known Navier-Stokes equations. The Navier-Stokes equations contain the conservation laws of mass and momentum, and describe the spatial-temporal change of the fluid velocity field. This thesis aims to investigate numerical solvers for the incompressible Navier-Stokes equations in two and three space dimensions. In particular, we focus on the second-order projection method introduced by Kim and Moin, which was extended from Chorin’s first-order projection method. We apply Fourier-Spectral methods for the periodic boundary condition. Numerically, we discretize the system using central differences scheme on Marker and Cell (MAC) grid spatially and the Crank-Nicolson scheme temporally. We then apply the fast Fourier transform to solve the resulting Poisson equations as sub-steps in the projection method. We will verify numerical accuracy and provide the stability analysis using von Neumann. In addition, we will simulate the particles' motion in the 2D and 3D fluid flow.

Author: D. Drikakis
Publisher: Springer Science & Business Media
ISBN: 354026454X
Category : Science
Languages : en
Pages : 623

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The study of incompressible ?ows is vital to many areas of science and te- nology. This includes most of the ?uid dynamics that one ?nds in everyday life from the ?ow of air in a room to most weather phenomena. Inundertakingthesimulationofincompressible?uid?ows,oneoftentakes many issues for granted. As these ?ows become more realistic, the problems encountered become more vexing from a computational point-of-view. These range from the benign to the profound. At once, one must contend with the basic character of incompressible ?ows where sound waves have been analytically removed from the ?ow. As a consequence vortical ?ows have been analytically “preconditioned,” but the ?ow has a certain non-physical character (sound waves of in?nite velocity). At low speeds the ?ow will be deterministic and ordered, i.e., laminar. Laminar ?ows are governed by a balance between the inertial and viscous forces in the ?ow that provides the stability. Flows are often characterized by a dimensionless number known as the Reynolds number, which is the ratio of inertial to viscous forces in a ?ow. Laminar ?ows correspond to smaller Reynolds numbers. Even though laminar ?ows are organized in an orderly manner, the ?ows may exhibit instabilities and bifurcation phenomena which may eventually lead to transition and turbulence. Numerical modelling of suchphenomenarequireshighaccuracyandmostimportantlytogaingreater insight into the relationship of the numerical methods with the ?ow physics.

Author: Rodolfo Salvi
Publisher: CRC Press
ISBN: 0824744896
Category : Mathematics
Languages : en
Pages : 337

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"Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."

Author: Alexandre Jo©·el Chorin
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 40

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