(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
In this paper, a new improved upwind technique for the moving least squares (MLS) method is proposed for solving convection dominated diffusion problems. The MLS approximation reconstructs a given function from randomly distributed data, which has been successfully applied to many meshless methods. To reduce spurious oscillations and improve accuracy, an upwind strategy with a limiter is designed for the MLS method. The method allows the reconstruction process to switch between different neighborhoods, several numerical examples are tested to confirm the feasibility of the proposed method. For the method, the convection term is approximated on the upwind recomstruction template and a limiter is used while the diffusion term is still approximated by a central reconstruction template. Numerical experiments are conducted to show the superiority and effectiveness of the high-resolution upwind MLS with limiter under a variety of convection dominated diffusion problems, and comparisons are made to see the advantages over some other methods.