Volume 1, Issue 5
Multiquadric Finite Difference (MQ-FD) Method and its Application

Yong Yuan Shan ,  Chang Shu and Ning Qin

10.4208/aamm.09-m0942

Adv. Appl. Math. Mech., 1 (2009), pp. 615-638.

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  • 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.

  • History

Published online: 2009-01

  • AMS Subject Headings

41A10, 41A30, 65N05

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