A fast and stabilized meshless method for the convection-dominated convection-diffusion problems

This paper presents a fast and stabilized meshless method that combines variational multi-scale element free Galerkin (VMEFG) method and proper orthogonal decomposition (POD) method, namely VMEFG&POD, to solve convection-diffusion problems. Variational multi-scale method is applied to overcome the numerical oscillation for the convection-dominated problems and the POD method is used to improve the computational efficiency of the VMEFG method. This method is validated by considering the simulation of two-dimensional convection-diffusion problems with a small diffusion coefficient. It is demonstrated that the proposed method can largely improve the computational efficiency without a significant loss in accuracy.