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Potential Flow (potential + flow)

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Selected Abstracts

Potential flow around obstacles using the scaled boundary finite-element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003
Andrew J. Deeks
Abstract The scaled boundary finite-element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one co-ordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) co-ordinate direction. These co-ordinate directions are defined by the geometry of the domain and a scaling centre. The method can be employed for both bounded and unbounded domains. This paper applies the method to problems of potential flow around streamlined and bluff obstacles in an infinite domain. The method is derived using a weighted residual approach and extended to include the necessary velocity boundary conditions at infinity. The ability of the method to model unbounded problems is demonstrated, together with its ability to model singular points in the near field in the case of bluff obstacles. Flow fields around circular and square cylinders are computed, graphically illustrating the accuracy of the technique, and two further practical examples are also presented. Comparisons are made with boundary element and finite difference solutions. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Transient deformation of a poroelastic channel bed

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2002
P.C. Hsieh
Abstract The coupled transient response of a poroelastic bed form due to stream flow and non-linear water waves is investigated numerically. The theory of potential flow is applied to channel flow while Biot's theory of poroelasticity (J. Appl. Phys. 1962; 33(4):1482) is adopted to deal with the deformable porous bed. A boundary-fitted co-ordinate system is used to calculate the variation in the bed form. The result of a simple periodic wave form over a soft poroelastic bed agrees well with the analytical solution of Hsieh et al. (J. Eng. Mech., ASCE 2000; 126(10):1064). However, due to the rapidly damping second dilatational wave inside the soft poroelastic bed, the solution for transient bed form near the interface is not easy to compute accurately. In order to overcome this difficulty, a simplified numerical model based on the boundary layer correction concept proposed by Hsieh et al. (2000) is established, which neglects Darcy's terms. The transient deformation of an irregular poroelastic bed that includes a trench and a downward step at the channel bed is simulated successfully. Copyright © 2002 John Wiley & Sons, Ltd. [source]

The formation of dunes, antidunes, and rapidly damping waves in alluvial channels

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2001
L.-H. Huang
Abstract Under the effect of a constant current for a long time, a water channel of infinitely long and constant depth interacting with a uniform sandbed of infinite thickness is used to simulate the formation of dunes, antidunes and rapidly damping waves in alluvial channels. The theory of potential flow is applied to the channel flow, while Biot's theory of poroelasticity is adopted to deal with erodible bed material. The governing equations, together with free surface, bed surface, and far field boundary conditions, form a complete boundary-value problem without applying empirical sediment discharge formulas as in conventional researches. The comparison of the present result with Kennedy's (Journal of Fluid Mechanics, 1963; 16: 521,544) instability analysis not only indicates the appropriateness of the present work, but also reveals the advantage of the present study due to its ability to find all kinds of bed forms (including the rapidly damping waves that Kennedy could not find) and of solving for the unclear lagged distance , introduced in Kennedy's work. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Treatment of Neumann boundaries in the complex variable boundary element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2004
Kozo Sato
Abstract For potential flow, the complex variable boundary element method (CVBEM) is formulated in terms of the velocity potential , and the stream function ,. In actual flow problems, , and ,,/,n are given along Dirichlet and Neumann boundaries, respectively. In the CVBEM, the Neumann-type condition ,,/,n is not directly handled, and, instead, , is used to define Neumann boundaries. Owing to this discrepancy, numerical difficulties are raised along Neumann boundaries. The current study addresses two such difficulties: (1) multiple Neumann boundaries and (2) branch cuts across Neumann boundaries. The first problem is due to the fact that , along multiple boundaries cannot be specified a priori, and the second problem is due to the discontinuous jump inherent in , for sink/source singularities. To overcome these difficulties, a new formulation of the CVBEM to solve for the unknown , values and a proper way of branch-cut placement are proposed, and these techniques are verified against example problems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Resolution of the flow in clarifiers by using a stabilized finite element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2004
P. Vellando
Abstract The description of the flow that takes place in clarifiers and other wastewater treatment basins may be a powerful tool to attain an optimum design of these structures, in order to make the most of the wastewater treatment plant resources. Some authors have attempted so by making use of the potential flow or the Stokes equations. When these simplifications are used, an approximation of the flow for slow creeping conditions is obtained, but only the resolution of the all-term-including Navier,Stokes equations will allow us to detect the real streamlines and the vortices that show up for even very slow water flows. The use of the Navier,Stokes formulae as the governing equations involves the appearance of complex stability problems that do not show up for the previously mentioned simplifications. In the present work a stable finite element method for the resolution of the Navier,Stokes equations is presented, verified, and used in the resolution of some wastewater treatment flow problems with very interesting results. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Potential flow around obstacles using the scaled boundary finite-element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003
Andrew J. Deeks
Abstract The scaled boundary finite-element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one co-ordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) co-ordinate direction. These co-ordinate directions are defined by the geometry of the domain and a scaling centre. The method can be employed for both bounded and unbounded domains. This paper applies the method to problems of potential flow around streamlined and bluff obstacles in an infinite domain. The method is derived using a weighted residual approach and extended to include the necessary velocity boundary conditions at infinity. The ability of the method to model unbounded problems is demonstrated, together with its ability to model singular points in the near field in the case of bluff obstacles. Flow fields around circular and square cylinders are computed, graphically illustrating the accuracy of the technique, and two further practical examples are also presented. Comparisons are made with boundary element and finite difference solutions. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Meshless numerical simulation of (full) potential flows in a nozzle by genetic algorithms

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2003
G. Winter
Abstract A new procedure to solve some fluid problems formulated in elliptical partial differential equations is presented. A Genetic Algorithm with a dynamical encoding and a partial grid sampling is proposed for it as the advantages of solving the problem without using all grid nodes at the same time, and of adjusting step grid, without increasing the complexity. The designed method has immediate applications some self-contained and some in combination with other traditional methods. Also, it provides a method alternative to the existing ones and uses simpler operations. Theoretical mathematical foundations of the problem are easily incorporated and that as a powerful characteristic of the method. In practice, our focus is to obtain an acceptable approximated solution. The method makes it possible to solveproblems with vague boundary conditions since no algebraic equation system is involved in the process. From the solution reached we have good information available to make an appropriate mesh to solve the problem through a traditional method. Comparative results for both linear and non-linear potential flow problems inside a nozzle are given. Copyright © 2003 John Wiley & Sons, Ltd. [source]