Unsymmetric and symmetric meshless schemes for the unsteady convection–diffusion equation

In this paper we investigate the application of unsymmetric and symmetric meshless collocation techniques with radial basis functions for solving the unsteady convection–diffusion equation. We employ the method of lines approach to discretize the governing operator equation. The stability of both explicit and implicit time-stepping schemes are analyzed. Numerical results are presented for 1D and 2D problems to compare the performance of the unsymmetric and symmetric collocation techniques. We compare the performance of various globally supported radial basis functions such as multiquadric, inverse multiquadric, Gaussian, thin plate splines and quintics. Numerical studies suggest that symmetric collocation is only marginally better than the unsymmetric approach. Further, it appears that both collocation techniques require a very dense set of collocation points in order to achieve accurate results for high Péclet numbers.