Some observations on unsymmetric radial basis function collocation methods for convection-diffusion problems

In this paper, we re-investigate the unsymmetric radial basis function (RBF) collocation method for solving convection–di usion problems with high P eclet number as in Power and Barraco (Computers and Mathematics with Applications 2002; 43:551). By testing di erent RBFs and di erent numbers of nodes, we found that the unsymmetric method can still solve high P eclet number problems reasonably well by using more nodes and domain decomposition techniques. Compared to solving one large problem, the domain decomposition method is shown to be very e cient and can improve the accuracy especially when the P eclet number is not that high. From our tests, it seems that the RBFs r4 ln r and r8 ln r are not very stable, while r6 ln r, r5 and r7 perform very well