Using Meshfree Weak-Strong Form Method for a 2-D Heat Transfer Problem

In this work, the numerical simulation of 2-D heat transfer problem is studied by using a meshfree method. The method is based on the local weak form collocation and the meshfree weak-strong (MWS) form. The goal of the paper is to find the temperature distribution in a rectangular plate. The results obtained are compared by those obtained by use of other numerical methods. Two types of boundary conditions are considered in this paper: Dirichlet and Neumann types. The Local Radial Point Interpolation Method (LRPIM) is used as the meshfree method. It is shown that the essential boundary conditions can be easily enforced as in the Finite Element Method (FEM), since the radial point interpolation shape functions posses the Kronecker delta property. It is also shown that the natural (derivative) boundary conditions can be satisfied by using the MWS method and no additional equation or treatment are needed. The MWS method as presented in this paper works well with local quadrature cells for nodes on the natural boundary and can be generated without any difficulty.