Meshless techniques for convection-diffusion problems

In this paper, the stability problem in the analysis of the convection-diffusion problem using meshfree methods is first discussed through an example problem of steady state convection-diffusion. Several techniques are then attempted to overcome the instability issues in convection dominated phenomenon simulated using meshfree collocation methods. These techniques include: the enlargement of the local support domain, upwind support domain, adaptive upwind support domain, and biased support domain. Numerical examples are presented to demonstrate the efficiency, accuracy and stability of the techniques proposed. Comparing with the conventional finite difference method (FDM) and the finite element method (FEM), the meshfree method has found some attractive advantages in solving the convection dominated problems in overcoming the instability problems.