Radial basis function meshless method for the steady incompressible Navier-Stokes equations

Authors:
Phani P. Chinchapatnam;K. Djidjeli;Prasanth B. Nair
Affiliations:
Computational Engineering and Design Group, University of Southampton, Southampton, UK;Computational Engineering and Design Group, University of Southampton, Southampton, UK;Computational Engineering and Design Group, University of Southampton, Southampton, UK
Venue:
International Journal of Computer Mathematics
Year:
2007

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Abstract

A meshless collocation method based on radial basis functions is proposed for solving the steady incompressible Navier-Stokes equations. This method has the capability of solving the governing equations using scattered nodes in the domain. We use the streamfunction formulation, and a trust-region method for solving the nonlinear problem. The no-slip boundary conditions are satisfied using a ghost node strategy. The efficiency of this method is demonstrated by solving three model problems: the driven cavity flows in square and rectangular domains and flow over a backward-facing step. The results obtained are in good agreement with benchmark solutions.