Solution of the Time-dependent, Incompressible Navier-stokes Equations Va̕ a Modified Finite Elements Method PDF Download
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Author: Philip M. Gresho
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Languages : en
Pages :
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Author: Philip M. Gresho
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Category :
Languages : en
Pages :
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Author: Guang Ren
Publisher:
ISBN:
Category : Finite element method
Languages : en
Pages : 16
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Author: Luigi Quartapelle
Publisher:
ISBN:
Category :
Languages : en
Pages : 154
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Author:
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Languages : en
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Future prospects regarding the numerical solution of the Navier-Stokes equations using the finite element method are discussed. Since the ultimate goal is to solve these equations in three-dimensions, only the primitive variable (u, P) formulation is considered. A novel feature of the two-dimensional solution technique relates to the methodology developed and employed for solving the semi-discretized system of ordinary differential equations, which are outlined in the section describing the development of the two-dimensional code. Following the discussion of numerical results from two-dimensional calculations, three-dimensional flows are discussed, where several potentially viable options are considered. (TFD).
Author: Roland Becker
Publisher:
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Category :
Languages : de
Pages : 115
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Author: Shrinivas G. Apte
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Category :
Languages : en
Pages :
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A primitive variable mixed order formulation of finite element method for solving three dimensional incompressible Navier-Stokes equations is presented. The method of weighted residuals is used for obtaining the approximate solutions of linear and nonlinear partial differential equations. The Physical domain is discretized by using unstructured tetrahedral elements. Unequal order interpolation functions are used for pressure & velocity variables while the temporal discretization is carried out by using an implicit time marching scheme based on finite differencing. One of the major diffculties arising during the finite element solution of an incompressible Navier-Stokes equations is the efficient factorization/preconditioning of the resulting indefinite stiffness matrix. In this work, the formation of an indefinite matrix is avoided by using a pseudo compressibility technique in which an artificial term is introduced into the mass matrix. The artificial term is time dependent and disposed at a later stage once the steady state is reached. Using this approach, the resulting system of equations can then be solved iteratively with standard preconditioners. The non-linear convective term in the Navier-Stokes equations is linearized in time. To diffuse the numerical oscillations which may occur in convection dominated flows, second-orderTaylor-Galerkinstabilization technique is used. The entire solution procedure is encoded in C++ using object oriented programming. One of the special features of this FEM code is that it uses the exact integrals of the shape functions in order to improve the accuracy of the solution, as supposed to any numerical integration schemes. The solution procedure is validated using the benchmark computations for 3D steady incompressible flows.
Author: Mutsuto Kawahara
Publisher: Springer
ISBN: 4431554505
Category : Technology & Engineering
Languages : en
Pages : 379
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This book focuses on the finite element method in fluid flows. It is targeted at researchers, from those just starting out up to practitioners with some experience. Part I is devoted to the beginners who are already familiar with elementary calculus. Precise concepts of the finite element method remitted in the field of analysis of fluid flow are stated, starting with spring structures, which are most suitable to show the concepts of superposition/assembling. Pipeline system and potential flow sections show the linear problem. The advection–diffusion section presents the time-dependent problem; mixed interpolation is explained using creeping flows, and elementary computer programs by FORTRAN are included. Part II provides information on recent computational methods and their applications to practical problems. Theories of Streamline-Upwind/Petrov–Galerkin (SUPG) formulation, characteristic formulation, and Arbitrary Lagrangian–Eulerian (ALE) formulation and others are presented with practical results solved by those methods.
Author: Bo-nan Jiang
Publisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 18
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Author: O. R. Sørensen
Publisher:
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Category :
Languages : en
Pages : 172
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Author: Fei Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 364
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