Spelling suggestions: "subject:"navierstokes equations"" "subject:"avierstokes equations""
11 
Modal finite element method for the navierstokes equationsSavor, Zlatko January 1977 (has links)
A modal finite element method is presented for the steady state and transient analyses of the plane flow of incompressible Newtonian fluid. The governing restricted functional is discretized with a high precision triangular stream function finite element. Eigenvalue analysis is carried out on the resulting discretized problem, under the assumption that the nonlinear convective term is equal to zero. After truncating at various levels of approximation to obtain a reduced number of modes, the transformation to the new vector space, spanned by these modes is performed. Advantage is taken of the ..symmetric and the antisymmetric properties of the modes in order to simplify the calculations. The Lagrange multipliers technique is employed to {incorporate the nonhomogeneous boundary conditions. The steady state analysis is carried out by utilizing the NewtonRaphson iterative procedure. The algorithm for transient analysis is based upon backward finite differences in time. Numerical results are presented for the fully developed plane Poiseuille flow, the flow in a square cavity, and the flow over a circular cylinder problems. These resultscfor the steady state are compared with the results obtained by direct finite element approach on the same grids and the results obtained by finite differences technique. It is concluded that the number of modes, which are to be retained in the analysis in order to achieve reasonable results, increases with the refinement of the finite element grid. Furthermore, the choice of modes to be used depends on the problem. Finally it is established, that this new modal method
yields good results in the range of moderate Reynolds numbers with about 50% or less of the modes of the problem. This, in turn, means that the time integrations can be performed on a greatly reduced number of equations and hence potential savings in computer time are significant. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

12 
Fully implicit solution of the NavierStokes equations and its application to nonrectangular geometry by the use of orthogonal mesh generation /Govenar, Robert Gerald January 1979 (has links)
No description available.

13 
Modeling fluid flow by exploring different flow geometries and effect of weak compressibilitySopko, James J. 06 1900 (has links)
Atmospheric mixing is a problem of exceptional importance and difficult to study. The anelastic approximation is the accepted fluid system governing the atmosphere over large vertical scales (about 8 km). The anelastic equations, unlike the NavierStokes equations, incorporate a nontrivial spatial divergence constraint on the velocity field. This yields a weakly compressible fluid flow. The basis of this study is to use numerical analysis to explore the effects of weak compressibility in the evolution of fluid governed by the anelastic equations, and the effects of incompressibility governed by the NavierStokes equation. The analysis then goes on to investigate the difference between three different initial conditions. Within each initial condition different density profiles are observed while varying parameters are investigated. Numerical results show that comparisons of incompressible NavierStokes equations to the anelastic fluid flow equations do not produce similar results. The weakly compressible flow creates a mixing barrier, stopping vertical fluid exchange. The perturbed middle region / US Navy (USN) author

14 
Regularity theory on axisymmetric incompressible NavierStokes equations.January 2013 (has links)
這篇論文將對三維不可壓納維  斯托克斯方程的軸對稱解的正則性理論作綜述。 / 在第一章會先重溫一些經典的正則性結果，例如用於 LerayHopf 弱解上的Serrin類條件和用於適當弱解上的CaffarelliKohnNirenberg 類理論。 / 第二章會處理假設為無漩的軸對稱解，由 Uchovskii 和Ladyzhenskaya 提出的整體正則解的唯一存在的結果將包含在其中。 / 從第三章起，解的漩將不再被假設為零，在這熱門的研究領域中，一些值得注意的結果會包含在論文之中。 / In this thesis, a survey on the regularity theory for axisymmetric solutions to the 3D incompressible NavierStokes equations is conducted. / In chapter 1, some classical results such as the Serrintype criteria on the LerayHopf weak solutions and the Ca arelliKohnNirenberg partial regularity theory on the suitable weak solutions to the equations are reviewed. / Chapter 2 deals with the axisymmetric solutions of the equations assuming the unknown velocity has no swirl. The existence result on the unique regular globalintime solution by Uchovskii and Ladyzhenskaya is included. / In chapter 3, the swirl component of the unknown velocity is no longer assumed to be zero and some remarkable results on this hot research area are presented and discussed in the thesis. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Lau, Tsz Ho. / Thesis (M.Phil.)Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 4951). / Abstracts also in Chinese. / Chapter 1  Classical Results on the 3D Incompressible NavierStokes Equations  p.3 / Chapter 1.1  Introduction  p.3 / Chapter 1.1.1  Backgrounds of the Equations  p.3 / Chapter 1.1.2  A Boundary Value Problem on Pressure  p.4 / Chapter 1.1.3  The HelmholtzLeray Decomposition  p.5 / Chapter 1.1.4  The Energy Equality  p.6 / Chapter 1.1.5  The LerayHopf Weak Solution  p.8 / Chapter 1.1.6  Foreword to the Regularity Problem  p.9 / Chapter 1.2  Serrin's Regularity Result  p.10 / Chapter 1.2.1  The Vorticity Form  p.11 / Chapter 1.2.2  Regularity of the Vorticity  p.12 / Chapter 1.2.3  The BiotSavart Law and Parabolic Regularity  p.13 / Chapter 1.2.4  Later Developments  p.14 / Chapter 1.3  CKN Partial Regularity Theory  p.14 / Chapter 1.3.1  Backgrounds and the Main Result  p.14 / Chapter 1.3.2  A Local Conditions for Regularity of u  p.16 / Chapter 1.3.3  The Blowup Estimate  p.19 / Chapter 1.3.4  Estimating the Singular Set  p.22 / Chapter 1.3.5  Later Developments  p.23 / Chapter 2  On Axially Symmetric Flows Without Swirl  p.25 / Chapter 2.1  Introduction and the Main Result  p.25 / Chapter 2.2  A Localintime Existence Result  p.26 / Chapter 2.3  A Priori Estimate  p.27 / Chapter 2.4  Proving the Global Existence Result  p.31 / Chapter 3  On Axially Symmetric Flows with Nonzero Swirl  p.32 / Chapter 3.1  Serrin's Type Regularity Conditions  p.32 / Chapter 3.1.1  Backgrounds and the Main Result  p.32 / Chapter 3.1.2  A Brief Discussion on the Proof  p.33 / Chapter 3.1.3  Later Developments  p.36 / Chapter 3.2  Lower Bound on the Blowup Rate  p.37 / Chapter 3.2.1  Backgrounds and the Main Result  p.37 / Chapter 3.2.2  Construction of Suitable Weak Solutions  p.38 / Chapter 3.2.3  Idea of the Proof  p.40 / Chapter 3.2.4  Later Developments  p.42 / Chapter 3.3  An Alternative Proof on Slow Blowup  p.43 / Chapter 3.3.1  Backgrounds and the Main Result  p.43 / Chapter 3.3.2  Liouville Type Theorems  p.44 / Chapter 3.3.3  The Rescaling Procedure  p.46 / Chapter 3.3.4  Later Developments  p.47

15 
On the incompressible NavierStokes equations and related systems.January 2013 (has links)
本文研究了不可壓NavierStokes 方程和其他相關係統的解的正則性，包括适当弱解和LerayHopf 弱解。 / 首先，我們考慮了不可壓穩態NavierStokes 方程和磁流体方程的適當弱解的部分正則性，包括內部和邊界情況。與五維情況不同，最關鍵的爆破方法在這種情況下不適用，我們用了靴帶法。但是對於邊界情況，在壓力的迭代中出現了困難項。為了克服它們，我們充分利用了改進的局部能量不等式並且找到了一個新的迭代量。這在本文定理的證明中起到了關鍵的作用。此外，這給我們提供了一種處理適當弱解的邊界正則性的新方法。 / 接著，我們得到了一些不依賴於磁場的四維磁流體方程的內部正則性準則。考慮到四維是臨界情況，我們仍然採用靴帶法。為了保證解的正則性準則不依賴於磁場，我們要做更精細的估計。 / 再次，对于三維轴对称磁流体方程，我們讨论了兩种LerayHopf弱解的正則性准則。利用标准的能量方法和爆破准則，我們得到了一些充分条件。这些条件保证了解的光滑性。 / 最後，對於帶有部分粘性的三維軸對稱磁流體方程，我們得到了LerayHopf 弱解的整體正則性。在部分粘性缺失的情況下，相關方向失了光滑性效應。在這種情況下，我們充分利用了磁流體的方程的特殊結構去彌補這個困難。 / In this thesis, we study the regularity of solutions to the incompressible Navier Stokes equations and other related systems, including both suitable weak solutions and LerayHopf weak solutions. / Firstly, we consider the partial regualrity of suitable weak solutions to the 6D steadystate NavierStokes and MHD equations, including both interior and boundary case. Be different from the five dimensional case, the key blowup arguments don't hold in this case, we use the bootstrap arguments instead. However, for the boundary case, hard terms appear in the interation of pressure. To overcome them, we make full use of the revised local energy inequality and find a new iteration quantity which plays a crucial role in the proof. Moreover, this provides a new method to deal with the boundary regularity of suitable weak solutions. / Secondly, we obtain some interior regularity criterias for the four dimensional MHD equations indepedent of magnetic field. Considering that four dimension is the critical case, we still use the bootstrap arguments. To guarantee that the criterias is independent of magnetic, we should do more subtle estimates. / Thirdly, we discuss two kinds of regularity criterias of LerayHopf weak solutions to 3D axisymmetric MHD equations. By use of standard energy method and blowup arguments, we derive some sufficient conditions which guarantee the smoothness of solutions. / Finally, we get the global regualrity of LerayHopf weak solutions of 3D axisymmetric MHD equations with partial viscosities. In the absence of partial viscosities, there is no smoothing effect on that directions. Under this circumstance, we take full advantage of the special structure of MHD equations to make up this shortcoming. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Liu, Jitao. / Thesis (Ph.D.)Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 132142). / Abstracts also in Chinese. / Introduction  p.4 / Chapter 1  Interior and Boundary Regularity Criterias for 6D SteadyState incompressible NavierStokes and MHD equations  p.17 / Chapter 1.1  Introduction  p.18 / Chapter 1.2  Notations  p.18 / Chapter 1.3  Interior Regualrity  p.20 / Chapter 1.3.1  Main results  p.20 / Chapter 1.3.2  Proof of Theorem 2.1.2  p.23 / Chapter 1.3.3  Proof of Theorem 2.1.3  p.27 / Chapter 1.3.4  Proof of Theorem 2.5.4  p.29 / Chapter 1.4  Boundary Regularity  p.36 / Chapter 1.4.1  Main Results  p.36 / Chapter 1.4.2  Some technical lemmas  p.39 / Chapter 1.4.3  Proof of Theorem 1.4.2  p.42 / Chapter 1.4.4  Proof of Proposition 1.4.8  p.45 / Chapter 2  Interior Regularity Criterias for the incompressible MHD Equations in four diemnsion  p.54 / Chapter 2.1  Introduction  p.55 / Chapter 2.2  Notations and some technical lemmas  p.57 / Chapter 2.3  Proof of Theorem 2.1.2: Estimates of the velocity  p.60 / Chapter 2.4  Proof of Theorem 2.1.3: Estimates of the gradient of the velocity  p.65 / Chapter 2.5  Proof of Proposition 2.1.4: "regularity  p.67 / Chapter 3  Regularity Criterias of the 3D axisymmetric MHD Equations  p.73 / Chapter 3.1  Introduction  p.74 / Chapter 3.2  Preliminaries  p.76 / Chapter 3.2.1  Notations  p.76 / Chapter 3.2.2  Some useful estimates  p.77 / Chapter 3.3  Proof of Theorem 3.1.1  p.82 / Chapter 3.4  Proof of Theorem 3.1.2 and 3.1.3  p.86 / Chapter 3.4.1  Proof of Theorem 3.1.2  p.86 / Chapter 3.4.2  Proof of Theorem 3.1.3  p.91 / Chapter 3.5  Proof of Theorem 3.1.4  p.94 / Chapter 4  Global regularity for the 3D axisymmetric MHD Equations with horizontal dissipation and vertical magnetic dicusion  p.103 / Chapter 4.1  Introduction  p.104 / Chapter 4.2  Notations and some technical lemmas  p.104 / Chapter 4.2.1  Notations  p.105 / Chapter 4.2.2  Some estimates about axisymmetric structure  p.106 / Chapter 4.2.3  Some estimates about partial viscosities  p.109 / Chapter 4.3  A Priori Estimates  p.110 / Chapter 4.3.1  L² and H¹ Estimates  p.110 / Chapter 4.3.2  H² Estimates  p.117 / Chapter 4.4  Proof of Theorem 4.1.1  p.126 / Chapter 5  Discussions on the Future Research  p.130 / Chapter 5.1  Incompressible NavierStokes equations  p.130 / Chapter 5.2  Incompressible MHD equations  p.131 / Bibliography  p.131

16 
Qualitative behavior of solutions to the compressible NavierStokes equations and its variants. / CUHK electronic theses & dissertations collectionJanuary 2004 (has links)
Li Jing. / "June 2004." / Thesis (Ph.D.)Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 6671). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

17 
Some qualitative studies on the solutions to the incompressible NavierStokes systems and related problems. / CUHK electronic theses & dissertations collectionJanuary 2004 (has links)
Zhou Yong. / "July 2004." / Thesis (Ph.D.)Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 105112). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

18 
Some results on blowup of solutions for the compressible NavierStokes equations. / CUHK electronic theses & dissertations collection / Digital dissertation consortiumJanuary 2009 (has links)
Finally, we prove a blow up criterion for the full compressible NavierStokes equations just in terms of the gradient of the velocity. / In this thesis, the author study the blowup of solutions for strong and classical solutions to the compressible NavierStokes equations. In the first part, we prove a blow up criterion for strong solutions to the compressible NavierStokes equations, similar to the BealKatoMajda criterion for the ideal incompressible flows. / The same criterion for classical solutions to the compressible NavierStokes equations is established in the second part of this thesis. In addition, initial vacuum is allowed in both cases. / Huang, Xiangdi. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 7309(E), Section: B. / Thesis (Ph.D.)Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 9096). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

19 
A numerical solution of the NavierStokes equation in a rectangular basinMay, Robert (Robert L.) January 1978 (has links) (PDF)
No description available.

20 
Numerical simulation of 2D flow past a dimpled cylinder using a pseudospectral methodKotovshchikova, Marina 08 January 2007 (has links)
A numerical simulation of steady and unsteady twodimensional flows past cylinder with dimples based on highly accurate pseudospectral method is the subject of the present thesis. The vorticitystreamfunction formulation of twodimensional incompressible NavierStokes equations with noslip boundary conditions is used. The system is formulated on a unit disk using curvilinear body fitted coordinate system. Key issues of the curvilinear coordinate transformation are discussed, to show its importance in properly defined node distribution. For the space discretization of the governing system the FourierChebyshev pseudospectral approximation on a unit disk is implemented. To handle the singularity at the pole of the unit disk the approach of defining the computational grid proposed by Fornberg was implemented. Two algorithms for solving steady and unsteady problems are presented. For steady flow simulations the nonlinear timeindependent NavierStokes problem is solved using the Newton's method. For the timedependent problem the semiimplicit third order AdamsBashforth/Backward Differentiation scheme is used. In both algorithms the fully coupled system with two noslip boundary conditions is solved. Finally numerical result for both steady and unsteady solvers are presented. A comparison of results for the smooth cylinder with those from other authors shows good agreement. Spectral accuracy is demonstrated using the steady solver. / February 2007

Page generated in 0.1515 seconds