Lack of conservation has been the biggest drawback in meshfree generalizedfinite difference methods (GFDMs). In this paper, we present a novelmodification of classical meshfree GFDMs to include local balances whichproduce an approximate conservation of numerical fluxes. This numerical fluxconservation is done within the usual moving least squares framework. UnlikeFinite Volume Methods, it is based on locally defined control cells, ratherthan a globally defined mesh. We present the application of this method to anadvection diffusion equation and the incompressible Navier - Stokes equations.Our simulations show that the introduction of flux conservation significantlyreduces the errors in conservation in meshfree GFDMs.
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