Performance of Multiquadric Collocation Method in Solving Lid-driven Cavity Flow Problem with Low Reynolds Number
S. Chantasiriwan

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 15, No. 3, pp. 137-146, 2006
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Keywords Navier-Stokes, Meshless, Multiquadrics, Radial basis function
Abstract The multiquadric collocation method is the collocation method based on radial basis function known as multiquadrics. It has been successfully used to solve several linear and nonlinear problems. Although fluid flow problems are among problems previously solved by this method, there is still an outstanding issue regarding the influence of the free parameter of multiquadrics (or the shape parameter) on the performance of the method. This paper provides additional results of using the multiquadric collocation method to solve the lid-driven cavity flow problem. The method is used to solve the problem in the stream function-vorticity formulation and the velocity-vorticity formulation. Two test problems are solved, and solutions are compared with exact and benchmark solutions. It is found that the shape parameter affects solutions for the stream function-vorticity formulation differently from solutions for the velocity-vorticity formulation.
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