A note on two upwind strategies for RBF-based grid-free schemes to solve steady convection-diffusion equations

In this paper, two radial basis function (RBF)-based local grid-free upwind schemes have been discussed for convection-diffusion equations. The schemes have been validated over some convection-diffusion problems with sharp boundary layers. It is found that one of the upwind schemes realizes the boundary layers more accurately than the rest. Comparisons with the analytical solutions demonstrate that the local RBF grid-free upwind schemes based on the exact velocity direction are stable and produce accurate results on domains discretized even with scattered distribution of nodal points. Copyright © 2009 John Wiley & Sons, Ltd.