Improved MLPG Method for Potential Flow Problem

This paper addresses the development of the meshless local Petrov–Galerkin (MLPG) method. Two major drawbacks of the MLPG method are high computational cost and difficulty in the imposition of essential boundary conditions. Moving least squares schemes (MLS) is mostly used in the MLPG method and has these two major drawbacks. New MLS variants, such as improved interpolating moving least squares, MLS with orthogonal basis functions, and modified weight function in the MLS have been explored in the literature. These MLS variants have been successfully employed in the other meshless methods. Each MLS variant resolves one of the two drawbacks of the traditional MLS scheme. The improved MLPG methods based on these new MLS schemes have been developed for the potential flow problem, and their performance has been analysed in this paper. The improved MLPG method based on MLS with orthogonal basis function and modified weight function is proposed in this paper; it is approximately 8% faster than the traditional MLPG with MLS, and it also enables the Kronecker delta property at the same convergence rate and accuracy level of the traditional MLPG method.