Discrete Singular Convolution–Finite Subdomain Method for the Solution of Incompressible Viscous Flows

Wan, Dongdong; Patnaik, B.S.V.; Wei, Guannan

doi:10.1006/jcph.2002.7089

Cited by 54 publications

(50 citation statements)

References 51 publications

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“…Zhao et al [10,11] analyzed the high-frequency vibration of plates and plate vibration under irregular internal support using DSC algorithm. Wan et al [17,18] studied some fluid mechanics problem using DSC method. Civalek [20][21][22][23][24] gives numerical solution to free vibration problem of rotating and laminated conical shells and nonlinear analysis of plates on elastic foundation.…”

Section: Discrete Singular Convolutionmentioning

confidence: 99%

Free vibration and bending analysis of circular Mindlin plates using singular convolution method

Cívalek

Ersoy

2008

Commun. Numer. Meth. Engng.

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SUMMARYCircular plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration and bending behavior of thick circular plates based on Mindlin plate theory. The approach developed is based on the discrete singular convolution method and the use of regularized Shannon's delta kernel. Frequency parameters, deflections and bending moments are obtained for different geometric parameters of the circular plate. Comparisons are made with existing numerical and analytical solutions in the literature. It is found that the DSC method yields accurate results for the free vibration and bending problems of thick circular plates.

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Section: Discrete Singular Convolutionmentioning

confidence: 99%

Free vibration and bending analysis of circular Mindlin plates using singular convolution method

Cívalek

Ersoy

2008

Commun. Numer. Meth. Engng.

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“…At lower values of postcritical Reynolds numbers the flow is still laminar. Because of the popularity of the present problem in terms of applications and importance a number of experimental and numerical results are available in the literature for flow past a square cylinder mounted in a confined channel [8][9][10][11][12][13] .…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Viscous Flow over a Square Cylinder Using Lattice Boltzmann Method

Perumal

Kumar

Dass

2012

ISRN Mathematical Physics

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This work is concerned with the lattice Boltzmann computation of two-dimensional incompressible viscous flow past a square cylinder confined in a channel. It is known that the nature of the flow past cylindrical obstacles is very complex. In the present work, computations are carried out both for steady and unsteady flows using lattice Boltzmann method. Effects of Reynolds number, blockage ratio, and channel length are studied in detail. As good care has been taken to include appropriate measures in the computational method, these results enjoy good credibility. To sum up, the present study reveals many interesting features of square cylinder problem and demonstrates the capability of the lattice Boltzmann method to capture these features.

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“…Compared with traditional methods (see, for instance, References [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]), it is more reliable (for example, it can avoid chaos [3]), more exible (for example, it can bridge the global methods and the local methods [2]) and, especially more accurate (for example, it is 10 10 times accurate than an important approach ENO [21]; it can also be more accurate than the pseudospectral method [12]). Why it can achieve extreme high accuracy has also been demonstrated in Reference [22].…”

Section: Introductionmentioning

confidence: 99%

“…Proposed in References [1][2][3][4], the discrete singular convolution (DSC) algorithm is a promising numerical method which has been successfully applied to resolve kinds of benchmark problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] some of which involve singularity [3], non-linearity [1], complex phase [20] or complex geometry and boundary conditions [16]. Compared with traditional methods (see, for instance, References [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]), it is more reliable (for example, it can avoid chaos [3]), more exible (for example, it can bridge the global methods and the local methods …”

Section: Introductionmentioning

confidence: 99%

Parameter optimization in the regularized Shannon's kernels of higher‐order discrete singular convolutions

Xiong

Zhao

2003

Commun. Numer. Meth. Engng.

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SUMMARYThe -type discrete singular convolution (DSC) algorithm has recently been proposed and applied to solve kinds of partial di erential equations (PDEs). With appropriate parameters, particularly the key parameter r in its regularized Shannon's kernel, the DSC algorithm can be more accurate than the pseudospectral method. However, it was previously selected empirically or under constrained inequalities without optimization. In this paper, we present a new energy-minimization method to optimize r for higher-order DSC algorithms. Objective functions are proposed for the DSC algorithm for numerical di erentiators of any di erential order with any discrete convolution width. Typical optimal parameters are also shown. The validity of the proposed method as well as the resulted optimal parameters have been veriÿed by extensive examples.

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Discrete Singular Convolution–Finite Subdomain Method for the Solution of Incompressible Viscous Flows

Cited by 54 publications

References 51 publications

Free vibration and bending analysis of circular Mindlin plates using singular convolution method

Free vibration and bending analysis of circular Mindlin plates using singular convolution method

Numerical Simulation of Viscous Flow over a Square Cylinder Using Lattice Boltzmann Method

Parameter optimization in the regularized Shannon's kernels of higher‐order discrete singular convolutions

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