A MESHLESS CONTROL VOLUME METHOD APPLICATIONS TO DIFFUSION AND ADVECTION-DIFFUSION PROBLEMS

A novel meshless numerical technique to solve problems in computational mechanics is introduced. in the interest of the distinct comparison between the new technique and the prior methods, the manuscript fully explains the theory of the technique. for the one and two-dimensional diffusion and one and two-dimensional advection-diffusion examples presented in this study, the solution technique is presented in details. being a meshless technique, the control volumes are arbitrary chosen, and they possess simple shapes which contrary to the existing control volume methods can overlap. the number of the points within each control volume, hence the degree of the interpolation can be different throughout the considered computational domain. since the control volumes are of simple shapes, the integrals can be readily evaluated. compared to the other methods including the exact solution, the results show to be highly accurate and very promising for a broad range of problems in computational mechanics