A Solution Procedure for Three-dimensional Incompressible Navier-Stokes Equation and Its Application PDF Download
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Author: Dochan Kwak
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Author: Dochan Kwak
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Author: Alexander Victor
Publisher:
ISBN:
Category :
Languages : en
Pages :
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One of the most important applications of finite difference lies in the field of computational fluid dynamics (CFD). In particular, the solution to the Navier-Stokes equation grants us insight into the behavior of many physical systems. The 2-D and 3-D incompressible Navier-Stokes equation has been studied extensively due to its analogous nature to many practical applications, and several numerical schemes have been developed to provide solutions dedicated to different environmental conditions (such as different Reynolds numbers). This research also covers the assignment of boundary conditions, starting with the simple case of driven cavity flow problem. In addition, several parts of the equations are given implicitly, which requires efficient ways of solving large systems of equations.We also considered numerical solution methods for the incompressible Navier-Stokes equations discretized on staggered grids in general coordinates. Numerical experiments are carried out on a vector computer. Robustness and efficiency of these methods are studied. It appears that good methods result from suitable combinations of multigrid methods.Numerically solving the incompressible Navier-Stokes equations is known to be time-consuming and expensive; hence this research presents some MATLAB codes for obtaining numerical solution of the Navier-Stokes equations for incompressible flow through flow cavities, using method of lines, in three-dimensional space (3-D). The code treats the laminar flow over a two-dimensional backward-facing step, and the results of the computations over the backward-facing step are in excellent agreement with experimental results.
Author: Jincheng Yang (Ph. D.)
Publisher:
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Category :
Languages : en
Pages : 0
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We show a series of works of some regularity results on the incompressible Navier-Stokes equation in dimension three. Using the blow-up method, we estimate the higher regularity in the Lorentz norm for smooth solutions to the Navier-Stokes equation. In particular, we show a second derivative estimate for suitable weak solutions, which improves the currently known regularity. We construct a maximal function associated with geometric objects that we call skewed cylinders, appearing in inviscid flows like the Eulerian cylinders around the Lagrangian trajectories. We also apply the blow-up method to estimate the boundary vorticity, which enables us to achieve an unconditional control of the layer separation of Leray-Hopf solutions from a steady shear flow in a finite periodic channel
Author: Stuart Eames Rogers
Publisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 52
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Author:
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Category : Aeronautics
Languages : en
Pages : 702
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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: Douglas A. Riley
Publisher:
ISBN:
Category :
Languages : en
Pages : 376
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Author: Giuseppe Da Prato
Publisher: Cambridge University Press
ISBN: 0521579007
Category : Mathematics
Languages : en
Pages : 355
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This is the only book on stochastic modelling of infinite dimensional dynamical systems.
Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781729191729
Category : Science
Languages : en
Pages : 50
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Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis. Jiang, Bo-Nan and Loh, Ching Y. and Povinelli, Louis A. Glenn Research Center NCC3-233; RTOP 505-90-5K
Author: Domenic Dambrosio
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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