Meshless RBF collocation for steady incompressible flows.

A meshless solver for the steady incompressible Navier-Stokes equations using radial basis functions is presented. The problem of implementing boundary conditions is circumvented using a ghost center strategy. A methodology for tuning the shape parameter in the present method is also presented. The nonlinear system of equations arising from spatial discretization is solved using a trust-region dogleg strategy. The meshless formulation is validated by solving the lid-driven cavity problem for different Reynolds numbers. Numerical results obtained with a small set of points are shown to be in very good agreement with the benchmark solution.