Development of least-square-based two-dimensional finite-difference schemes and their application to simulate natural convection in a cavity

Ding, Hang; Chen, Shu; Yeo, K. S.; Xu, Dongsheng

doi:10.1016/s0045-7930(03)00036-7

Cited by 93 publications

(83 citation statements)

References 12 publications

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“…1. The above equations (9) being an over-determined system, least squares technique [7,2] to approximate the unknown gradient vector is suggested. Here, we have chosen a 3 point stencil for estimating one derivative.…”

Section: Weighted Least Squares Formulationmentioning

confidence: 99%

“…In order to incorporate differences in the influence of each neighbouring point on the gradient (which is usually based on distance from the node), the least squares method needs to be modified. This was achieved by modifying equation (11) with the introduction of a diagonal matrix (called weight matrix) to yield the weighted least squares approximation [7],…”

Section: Weighted Least Squares Formulationmentioning

confidence: 99%

“…Similar to the approach followed in Section 4 for 1D, the unknown gradients can then be obtained from the above system (23) using weighted least squares formulation [7] as…”

Section: Extension Of Sdwls To Two Dimensionsmentioning

confidence: 99%

“…The weights (diagonal entries of W) used in literature are geometric quantities, typically of the form w j = 1/(|r i − r j | a ) with a taking the values 0, 1, 2 [7,2,15]; where r i and r j are the displacement vectors of the centroids of cell i and j respectively.…”

Section: Extension Of Sdwls To Two Dimensionsmentioning

confidence: 99%

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On the link between weighted least-squares and limiters used in higher-order reconstructions for finite volume computations of hyperbolic equations

Mandal

Subramanian

2008

Applied Numerical Mathematics

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Section: Weighted Least Squares Formulationmentioning

confidence: 99%

Section: Weighted Least Squares Formulationmentioning

confidence: 99%

“…Similar to the approach followed in Section 4 for 1D, the unknown gradients can then be obtained from the above system (23) using weighted least squares formulation [7] as…”

Section: Extension Of Sdwls To Two Dimensionsmentioning

confidence: 99%

Section: Extension Of Sdwls To Two Dimensionsmentioning

confidence: 99%

See 2 more Smart Citations

On the link between weighted least-squares and limiters used in higher-order reconstructions for finite volume computations of hyperbolic equations

Mandal

Subramanian

2008

Applied Numerical Mathematics

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“…The semi-discrete equation (28) can be solved by explicit schemes such as Runge-Kutta method. But the convergence rate of explicit schemes is very slow.…”

Section: Upwind Enforced Semi-discrete Form Of Euler Equationsmentioning

confidence: 99%

An Efficient Implicit Mesh-Free Method to Solve Two-Dimensional Compressible Euler Equations

Chen

2005

Int. J. Mod. Phys. C

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Local radial basis function-based differential quadrature (RBF-DQ) method is a natural mesh-free approach, in which any derivative of a function at a point is approximated by a weighted linear sum of functional values at its surrounding scattered points. In this paper, the weighting coefficients in the spatial derivative approximation of the Euler equation are determined by using a weighted least-square procedure in the frame of RBFs, which enhances the flexibility of distributing points in the computational domain. An upwind method is further introduced to cope with discontinuities by using Roe's approximate Riemann solver for estimation of the inviscid flux on the virtual mid-point between the reference knot and its surrounding knot. The lower-upper symmetric GaussSeidel (LU-SGS) algorithm, which is implemented in a matrix-free form like the one used in the finite-volume method, is introduced in the work to speed up the convergence. The proposed approach is validated by its application to simulate transonic flows over a NACA 0012 airfoil. It was found that the present mesh-free results agree very well with available data in the literature, and the implicit LU-SGS algorithm can greatly save the computational time as compared with explicit time marching methods.

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Processing the image gradient field using a topographic primal sketch approach

Gambaruto

2015

Numer Methods Biomed Eng

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Processing the image gradient field using a topographic primal sketch approachComputer Applications in Science & Engineering (CASE) Nexus I -Campus Nord UPC, C/ Jordi Girona 2, 08034 Barcelona, Spain AbstractThe spatial derivatives of the image intensity provide topographic information that may be used to identify and segment objects. The accurate computation of the derivatives is often hampered in medical images by the presence of noise and a limited resolution. This paper focuses on accurate computation of spatial derivatives and their subsequent use to process an image gradient field directly, from which an image with improved characteristics can be reconstructed. The improvements include noise reduction, contrast enhancement, thinning object contours and the preservation of edges.Processing the gradient field directly instead of the image is shown to have numerous benefits. The approach is developed such that the steps are modular, allowing the overall method to be improved and possibly tailored to different applications. As presented, the approach relies on a topographic representation and primal sketch of an image.Comparisons with existing image processing methods on a synthetic image and different medical images show improved results and accuracy in segmentation. Here the focus is on objects with low spatial resolution, which is often the case in medical images. The methods developed show the importance of improved accuracy in derivative calculation, and the potential in processing the image gradient field directly.

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Development of least-square-based two-dimensional finite-difference schemes and their application to simulate natural convection in a cavity

Cited by 93 publications

References 12 publications

On the link between weighted least-squares and limiters used in higher-order reconstructions for finite volume computations of hyperbolic equations

On the link between weighted least-squares and limiters used in higher-order reconstructions for finite volume computations of hyperbolic equations

An Efficient Implicit Mesh-Free Method to Solve Two-Dimensional Compressible Euler Equations

Processing the image gradient field using a topographic primal sketch approach

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