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

作者：Shan Yong Yuan; Shu Chang^*; Qin Ning

来源：Advances in Applied Mathematics and Mechanics, 2009, 1(5): 615-638.

DOI：10.4208/aamm.09-m0942

• MQ-FD method
• shape parameter
• central FD method

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.

• 出版日期2009-10