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|Title:||Multiquadric finite difference (MQ-FD) method and its application|
|Keywords:||Central FD method.|
|Source:||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|
|Appears in Collections:||Staff Publications|
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