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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.