A meshfree method for incompressible fluid dynamics problems

We show that meshfree variational methods may be used for the solution of incompressible uid dynamics problems using the R-function method (RFM). The proposed approach constructs an approximate solution that satis es all prescribed boundary conditions exactly using approximate distance elds for portions of the boundary, trans nite interpolation, and computations on a non-conforming spatial grid. We give detailed implementation of the method for two common formulations of the incompressible uid dynamics problem: rst using scalar stream function formulation and then using vector formulation of the Navier–Stokes problem with arti cial compressibility approach. Extensive numerical comparisons with commercial solvers and experimental data for the benchmark back-facing step channel problem reveal strengths and weaknesses of the proposed meshfree method