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Three-dimensional Viscous Flow (three-dimensional + viscous_flow)

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Engineering80%

Selected Abstracts

Three-dimensional viscous flow over rotating periodic structures

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003
Kyu-Tae Kim
Abstract The three-dimensional Stokes flow in a periodic domain is examined in this study. The problem corresponds closely to the flow inside internal mixers, where the flow is driven by the movement of a rotating screw; the outer barrel remaining at rest. A hybrid spectral/finite-difference approach is proposed for the general expansion of the flow field and the solution of the expansion coefficients. The method is used to determine the flow field between the screw and barrel. The regions of elongation and shear are closely examined. These are the two mechanisms responsible for mixing. Besides its practical importance, the study also allows the assessment of the validity of the various assumptions usually adopted in mixing and lubrication problems. Copyright © 2003 John Wiley & Sons, Ltd. [source]

On singularities in the solution of three-dimensional Stokes flow and incompressible elasticity problems with corners

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004
A. Dimitrov
Abstract In this paper, a numerical procedure is presented for the computation of corner singularities in the solution of three-dimensional Stokes flow and incompressible elasticity problems near corners of various shape. For obtaining the order and mode of singularity, a neighbourhood of the singular point is considered with only local boundary conditions. The weak formulation of this problem is approximated using a mixed u, p Galerkin,Petrov finite element method. Additionally, a separation of variables is used to reduce the dimension of the original problem. As a result, the quadratic eigenvalue problem (P+,Q+,2R)d=0 is obtained, where the saddle-point-type matrices P, Q, R are defined explicitly. For a numerical solution of the algebraic eigenvalue problem an iterative technique based on the Arnoldi method in combination with an Uzawa-like scheme is used. This technique needs only one direct matrix factorization as well as few matrix,vector products for finding all eigenvalues in the interval ,,(,) , (,0.5, 1.0), as well as the corresponding eigenvectors. Some benchmark tests show that this technique is robust and very accurate. Problems from practical importance are also analysed, for instance the surface-breaking crack in an incompressible elastic material and the three-dimensional viscous flow of a Newtonian fluid past a trihedral corner. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A promising boundary element formulation for three-dimensional viscous flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005
Xiao-Wei Gao
Abstract In this paper, a new set of boundary-domain integral equations is derived from the continuity and momentum equations for three-dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex-variable technique is used to compute the divergence of velocity for internal points, while the traction-recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Non-perturbative solution of three-dimensional Navier,Stokes equations for the flow near an infinite rotating disk

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2010
Ahmet Y
Abstract In this paper, we present Homotopy perturbation method (HPM) and Padé technique, for finding non-perturbative solution of three-dimensional viscous flow near an infinite rotating disk. We compared our solution with the numerical solution (fourth-order Runge,Kutta). The results show that the HPM,Padé technique is an appropriate method in solving the systems of nonlinear equations. The mathematical technique employed in this paper is significant in studying some other problems of engineering. Copyright © 2009 John Wiley & Sons, Ltd. [source]

A promising boundary element formulation for three-dimensional viscous flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005
Xiao-Wei Gao
Abstract In this paper, a new set of boundary-domain integral equations is derived from the continuity and momentum equations for three-dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex-variable technique is used to compute the divergence of velocity for internal points, while the traction-recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations. Copyright © 2004 John Wiley & Sons, Ltd. [source]