High-Resolution Upwind Strategy for the MLS Method with Applications to Convection Dominated Diffusion Problems (Advances in Applied Mathematics and Mechanics, 2025)
In this paper, a new improved upwind technique for the moving leastsquares (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. Toreduce spurious oscillations and improve accuracy, an upwind strategy with a limiter is designed for the MLS method. The method allows the reconstruction processto switch between different neighborhoods, several numerical examples are tested toconfirm the feasibility of the proposed method. For the method, the convection termis approximated on the upwind recomstruction template and a limiter is used whilethe 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 dominateddiffusion problems, and comparisons are made to see the advantages over some othermethods.