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 a...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 MQFD 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.展开更多
文摘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 MQFD 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.
