Abstract: In this study, two local meshless methods: the Local Direct Meshless Method (LDR) and the Local Indirect Meshless Method (LiDR), are comprehensively compared for numerically approximating convection-diffusion partial differential types of equations (PDEs). Unlike other conventional collocation-related meshless methods, where the typical choice of radial basis function (RBF) is the famous Gaussian one, this work focuses on an alternative called the multiquadric RBF. The investigation tests, monitors, and records several parameters and their influences on the methods’ performances using 4 benchmarking test cases. It has been revealed that the LDR is capable of providing more consistent, better accuracy, especially over a wide range of durations and varying node configurations. The LiDR, on the other hand, is found to yield reasonable but less accurate solutions, particularly in the convection-dominated scenarios. Other than this, the work also provides useful insights regarding the effects of the shape parameter and the size of the subdomain, where the LDR’s improved performance makes it more promising for practical applications, which may include those related to engineering processes and environmental challenges. These findings contribute to the understanding of local meshless methods for solving convection-diffusion PDEs and offer valuable guidance for method optimization and future research.

Keywords: Differential Quadrature, Local Integration, Radial Basis Function, Multiquadric, Meshless Method, Convection-Diffusion

Pages: 287-305