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Multiquadric Finite Difference (MQ-FD) Method and Its Application

Multiquadric Finite Difference (MQ-FD) Method and Its Application
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Year:    2009

Author:    Yong Yuan Shan, Shu Chang, Ning Qin

Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 5 : pp. 615–638

Abstract

The conventional finite difference (FD) schemes are based on the low order polynomial approximation in a local region. This paper shows that when the polynomial approximation is replaced by the multiquadric (MQ) function approximation in the same region, a new FD method, which is termed as MQ-FD method in this work, can be developed. The paper gives analytical formulas of the MQ-FD method and carries out a performance study for its derivative approximation and solution of Poisson equation and the incompressible Navier-Stokes equations. In addition, the effect of the shape parameter $c$ in MQ on the formulas of the MQ-FD method is analyzed. Derivative approximation in one-dimensional space and Poisson equation in two-dimensional space are taken as model problems to study the accuracy of the MQ-FD method. Furthermore, a lid-driven flow problem in a square cavity is simulated by the MQ-FD method. The obtained results indicate that this method may solve the engineering problem very accurately with a proper choice of the shape parameter $c$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.09-m0942

Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 5 : pp. 615–638

Published online:    2009-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    MQ–FD method shape parameter central FD method.

Author Details

Yong Yuan Shan

Shu Chang

Ning Qin

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