A MESHLESS METHOD BASED ON FIRST ORDER TAYLOR SERIES AND WEIGHTED LEAST SQUARE METHOD

Abstract

In recent years, meshless methods are drawing increasing attentions due to its certain advantages over mesh-based methods. The absence of meshes gives meshless methods an edge in multi-dimensional problems and large deformation problems. Smoothed-Particle Hydrodynamics (SPH), Moving Particle Semi-implicit (MPS) method and Consistent Particle Method (CPM) are three well-established meshless methods, among which CPM is the newest. A meshless method based on the first order Taylor series and Weighted Least Square Method is formulated in this thesis as a variation or simplification of the original CPM. In the present method, the gradient operator is discretised into a three-dimensional array and scalar linear differential operators are discretised into square matrices. Several testing problems are conducted with verification by theoretical solution or experimental image.