Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows

Mai‐Duy, N.; Tran-Cong, T.

doi:10.1016/j.compstruc.2008.09.004

Cited by 8 publications

(6 citation statements)

References 31 publications

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“…It can be seen that (24) is a special case of (29), where f is simply set to null. By substituting Equation (29)…”

Section: One-dimensional Integrated Radial Basis Function Networkmentioning

confidence: 99%

“…The orders of convergence are 2.42, 2.61 and 2.92 for the minimum horizontal velocity u min , the maximum vertical velocity v max and the minimum vertical velocity v min along the center lines, respectively. The present results for a grid of 101 × 101 are more accurate than those of FDMs with more refined grids [1,28], but less than those of 1D-IRBFN [29]. Table 7 describes comparisons of the number of nonzero elements per row of the system matrix (N nzpr ), number of iterations (N iteration ) and total CPU time (T total ) required to obtain the converged solution with T OL = 10 −12 .…”

Section: Example 3: Lid-driven Cavity Flowmentioning

confidence: 99%

“…It is noted that the Neumann boundary conditions (92) can be imposed directly through the conversion process (26)(27)(28)(29). Therefore, we just need to consider the Poisson problem with Dirichlet boundary condition here.…”

Section: Non-overlapping Domain Decomposition Techniquementioning

confidence: 99%

“…Table 6 shows the grid convergence study of the extrema of the horizontal and vertical velocity profiles along the center lines of the cavity for Approach 1 in comparison with FDMs [1,28] and 1D-IRBFN [29]. The second-order accurate central finite-difference approximation was employed to approximate the linear terms in both FDMs mentioned above [1,28], while the nonlinear convection terms were discretised by using a first-order accurate upwind difference scheme including its second-order accurate term as a deferred correction in FDM [1] and uncentered second-order differences in FDM [28].…”

Section: Example 3: Lid-driven Cavity Flowmentioning

confidence: 99%

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Local moving least square‐one‐dimensional integrated radial basis function networks technique for incompressible viscous flows

Ngo-Cong

Mai‐Duy

Karunasena

et al. 2012

Numerical Methods in Fluids

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This paper presents a local moving least square -one-dimensional integrated radial basis function networks (LMLS-1D-IRBFN) method for solving incompressible viscous flow problems using stream function-vorticity formulation. In this method, the partition of unity method is employed as a framework to incorporate the moving least square (MLS) and one-dimensional integrated radial basis function networks (1D-IRBFN) techniques. The major advantages of the proposed method include: (i) a banded sparse system matrix which helps reduce the computational cost; (ii) the Kronecker-δ property of the constructed shape function which helps impose the essential boundary condition in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of integration instead of conventional differentiation to construct the local RBF approximations. Several examples including two-dimensional Poisson problems, lid-driven cavity flow and flow past a circular cylinder are considered and the present results are compared with the exact solutions and numerical results from other methods in the literature to demonstrate the attractiveness of the proposed method.

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“…It can be seen that (24) is a special case of (29), where f is simply set to null. By substituting Equation (29)…”

Section: One-dimensional Integrated Radial Basis Function Networkmentioning

confidence: 99%

Section: Example 3: Lid-driven Cavity Flowmentioning

confidence: 99%

Section: Non-overlapping Domain Decomposition Techniquementioning

confidence: 99%

Section: Example 3: Lid-driven Cavity Flowmentioning

confidence: 99%

See 2 more Smart Citations

Local moving least square‐one‐dimensional integrated radial basis function networks technique for incompressible viscous flows

Ngo-Cong

Mai‐Duy

Karunasena

et al. 2012

Numerical Methods in Fluids

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“…Due to the approximation process based on integration technique rather than conventional differentiation, it does not require the basis function to be differentiable or continuous. So far, many basis functions are available to incorporate into the present formulation, such as Haar wavelet, [11][12][13] Chebyshev polynomials, [14][15][16] radial basis function, 17,18 and so on. Moreover, in order to investigate the strain and stress fields of structures, the approximation of multi-order derivatives of displacements needs a considerably smooth quality.…”

Section: Introductionmentioning

confidence: 99%

An integrated spectral collocation approach for the static and free vibration analyses of axially functionally graded nonuniform beams

Xie

Zheng

Zou

2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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A spectral collocation approach based on integrated polynomials is presented to investigate the statics and free vibrations of Euler–Bernoulli beams with axially variable cross section, modulus of elasticity, and mass density. The basic concept of the approach is the expansion of the highest derivatives appearing in the governing equations instead of the solution function itself by the truncated basis function. Then lower order derivatives and the function itself are obtained by integration. The constants appearing from the integrating process are determined by given classical or elastic restrained boundary conditions. Also, by incorporating the decomposition technique into the present approach, higher order vibration modes can be achieved even for stepped beams. Numerical examples including the statics and free vibrations of the beams with variance in geometry or material have been successfully solved, and the results are compared with those analytical or numerical solutions in the existing literature. The convergence and comparison studies show that convergent speed is rather rapid and the present approach can yield high accurate results with low computational efforts. Furthermore, the accuracy is not particularly affected by the adopted polynomials.

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ADI method based onC2-continuous two-node integrated-RBF elements for viscous flows

An-Vo

Mai‐Duy

Tran

et al. 2013

Applied Mathematical Modelling

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Integrated radial-basis-function networks for computing Newtonian and non-Newtonian fluid flows

Cited by 8 publications

References 31 publications

Local moving least square‐one‐dimensional integrated radial basis function networks technique for incompressible viscous flows

Local moving least square‐one‐dimensional integrated radial basis function networks technique for incompressible viscous flows

An integrated spectral collocation approach for the static and free vibration analyses of axially functionally graded nonuniform beams

ADI method based onC2-continuous two-node integrated-RBF elements for viscous flows

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