Multiquadric Finite Difference (MQ FD) Method and its Application
The conventional finite difference (FD) schemes are based on the low or der polynomial approximation in a local region. This paper shows that when the polynomial approximation is replaced by the multiquadric (MQ) function approx imation 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.