A meshfree method for incompressible fluid dynamics problems

TLDR: In this article, mesh-free variational methods are used for the solution of incompressible fluid dynamics problems using the R-function method (RFM), which constructs an approximate solution that satisfies all prescribed boundary conditions exactly using approximate distance fields for portions of the boundary, transfinite interpolation, and computations on a non-conforming spatial grid.

Abstract: We show that meshfree variational methods may be used for the solution of incompressible fluid dynamics problems using the R-function method (RFM). The proposed approach constructs an approximate solution that satisfies all prescribed boundary conditions exactly using approximate distance fields for portions of the boundary, transfinite interpolation, and computations on a non-conforming spatial grid. We give detailed implementation of the method for two common formulations of the incompressible fluid dynamics problem: first using scalar stream function formulation and then using vector formulation of the Navier-Stokes problem with artificial 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.