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

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.

Keywords:

• Meshfree
• Meshless
• Radial basis functions
• Navier–Stokes
• Convection