A point collocation scheme for the stationary incompressible Navier-Stokes equations
Bull. Korean Math. Soc. 2013 Vol. 50, No. 5, 1737-1751
Printed September 1, 2013
Yongsik Kim
Ajou University
Abstract : An efficient and stable point collocation scheme based on a meshfree method is studied for the stationary incompressible Navier-Stokes equations. We describe the diffuse derivatives associated with the moving least square method. Using these diffuse derivatives, we propose a point collocation method to fit in solving the Navier-Stokes equations which improves the stability of the direct point collocation scheme. The convergence of the numerical solution is investigated from numerical examples. The driven cavity flow and the backward facing step flow are implemented for the reliability of the scheme. Also, the viscous flow on complicated geometry is successfully calculated such as the flow past a circular cylinder in duct.
Keywords : point collocation method, meshfree approximation, Navier-Stokes equations
MSC numbers : Primary 65N35, 76M25
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