Finite-Analytic Numerical Solution of Heat Transfer in Two-Dimensional Cavity Flow

Chen, Ching-Jen; Naseri-Neshat, H.; Ho, Kuo-San

doi:10.1080/10407798108547043

Cited by 9 publications

(9 citation statements)

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“…Such an approximation also results in damping out the small wavelengths important to describing a sharp concentration front. Since FA method has been reasonably successful in solving unsteady Navier-Stokes equations [Chen and Chen, 1984a, b;Chen and Cheng, 1984; and heat transfer equations [Chen et al, 1981;Chen and Li, 1979], the purpose of this paper is to present the results of using FA method for solving solute transport equation in groundwater.…”

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confidence: 99%

Finite Analytic Numerical Solution for Two‐Dimensional Groundwater Solute Transport

Hwang¹,

Chen²,

Sheikhoslami³

et al. 1985

Water Resources Research

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A new numerical method called the finite analytic (FA) method is used to solve a groundwater solute transport problem. The basic idea of the finite analytic method is the incorporation of local analytic solution in the numerical solution of the partial differential equation. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in an element and its neighboring nodal points. The assemble of the linear system equations results in a tridiagonal matrix. Like most finite difference method, the advantages of using efficient iterative techniques for solving tridiagonal matrices are equally applicable to FA method. The automatic localized upstream shift and the analytic property of the FA method eliminates the difficulty of numerical dispersion locally and suppresses the overall numerical dispersion for large Peclet number. For small Peclet number FA method yields excellent results in comparison with the analytic solution. For large Peclet number FA solutions are oscillation free with some degree of numerical dispersion. The results are comparable with those obtained using upstream weighted finite element method. INTRODUCTION This paper employs a new numerical method called the finite analytic (FA) method to study the two-dimensional solute transport in groundwater. The FA method was introduced by Chen and Li [1979] and Chen et al. [1981] to solve heat transfer problems. The method is neither a finite difference (FD) method nor a finite element (FE) method. The basic idea of the FA method is to invoke the analytic solution of the governing differential equation in the numerical solution of the problem. In the FA method the total problem is subdivided into small elements. The local analytical solution is then expressed in an algebraic form, relating an interior nodal value to its neighboring nodal values. The system of algebraic equations derived from the local solution is then solved to provide the solution of the total problem. Satisfactory numerical solution of groundwater solute transport equation can generally be obtained for small Peclet number (Pe = VL/D). However, for large Pe (e.g., small D) the numerical solutions characteristically exhibit either oscillations in concentration in the neighborhood of a sharp front or a smearing of the front. Thus numerical methods are often evaluated in terms of frontal smearing and concentration overshoot in the numerical solutions.Gray and Pinder [1976] assumed that the spatial distribution of concentration can be expressed as a Fourier series with components of different wavelengths. When the numerical dissipation (numerically induced errors that arise in computing the amplitude of the Fourier components) is large, the small wavelengths important to describing a sharp concentration front are damped out and the front is smeared. Large numerical dispersion (errors in a numerical solution caused by propagating a Fourier component at an incorrect speed) causes small wavelength to be out of phase with the la...

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confidence: 99%

Finite Analytic Numerical Solution for Two‐Dimensional Groundwater Solute Transport

Hwang¹,

Chen²,

Sheikhoslami³

et al. 1985

Water Resources Research

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“…The grid sizes in Figures 20 and 21 are all effective grid numbers. Nine-point and five-point finite analytic schemes are utilized to discretize the Navier -Stokes equations on regular and irregular elements, respectively [10,14]. Figure 20 gives the central velocity distributions and the convergent history.…”

Section: Solutions Of a Rotated Lid-dri6en Ca6ity Flowmentioning

confidence: 99%

Automatic grid generation of complex geometries in Cartesian co-ordinates

Lin

Chen

1998

Int. J. Numer. Meth. Fluids

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“…In fact, the literature review shows that two categories of studies were investigated [3]. The first category is concerned with a horizontal sliding lid, which encompasses the top wall [4][5][6][7][8], bottom-sliding wall [9], or an oscillating lid [10][11][12]. The second category is related with side driven differentially heated enclosures, where one wall or both vertical walls move with a constant speed [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of 2-D Incompressible Driven Cavity Flow with Wavy Bottom Surface

Uddin

Saha²

2015

AJAM

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Abstract:In the present numerical study is devoted to investigate the lid-driven cavity flow with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no-slip. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), and the number of undulations (λ) on the flow structures are investigated in detail. The behavior of the force coefficient C f also has been examined. Streamline plots provide the details of fluid flow. The fluid contained inside a squared cavity is set into motion by the top wall which is sliding at constant velocity from left to right and the undulation which was induced at the bottom surface. It is found that these parameters have significant effect on the flow fields in the cavity. Furthermore, the trends of skin friction for different values of the aforementioned parameters are presented in this investigation.

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Finite-Analytic Numerical Solution of Heat Transfer in Two-Dimensional Cavity Flow

Cited by 9 publications

References 0 publications

Finite Analytic Numerical Solution for Two‐Dimensional Groundwater Solute Transport

Finite Analytic Numerical Solution for Two‐Dimensional Groundwater Solute Transport

Automatic grid generation of complex geometries in Cartesian co-ordinates

Numerical Solutions of 2-D Incompressible Driven Cavity Flow with Wavy Bottom Surface

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