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Title: Multiquadric finite difference (MQ-FD) method and its application
Authors: Shan, Y.Y.
Shu, C. 
Qin, N.
Keywords: Central FD method.
MQ-FD method
Shape parameter
Issue Date: 2009
Citation: Shan, Y.Y.,Shu, C.,Qin, N. (2009). Multiquadric finite difference (MQ-FD) method and its application. Advances in Applied Mathematics and Mechanics 1 (5) : 615-638. ScholarBank@NUS Repository.
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. © 2009 Global Science Press.
Source Title: Advances in Applied Mathematics and Mechanics
ISSN: 20700733
Appears in Collections:Staff Publications

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