An improvement in MPS method using Voronoi diagram and a new kernel function

In this study, accuracy of the mesh-less moving particles semi-implicit (MPS) method in solving 2-D elliptic partial differential equations over a unit square domain with known analytical solutions is improved using Voronoi diagram drawing technique to approximate nodal volumes and a new kernel function. Voronoi diagram is employed as an alternative method for estimation of nodal volumes instead of kernel approximations. In addition to this, a kernel function with flat shape is introduced to enhance accuracy of MPS method. The numerical results obtained over highly irregular computational node distributions for the proposed kernel function show higher accuracy in comparison with two other employed kernel functions having steeper shapes.