Application of DRM-Trefftz and DRM-MFS to Transient Heat Conduction Analysis

In this article we present two numerical models for solving transient heat conduction problems. One is based on dual reciprocity method and Trefftz method (dubbed DRM-Trefftz), and the other is based on dual reciprocity method and fundamental solution (dubbed DRM-MFS). A time stepping method is used in handling the time variable to convert the problem into a set of inhomogeneous modified Helmholtz equations. The solution of the modified Helmholtz equation is divided into two parts, i.e. the particular solution and the homogeneous solution. While the particular solution is solved by DRM in which the source term is approximated by radial basis functions (RBF), the homogeneous solution is obtained by using MFS or Trefftz method. Two types of bases functions, Trefftz solution and Fundamental solution are used to approximate the homogeneous solution. The proposed two meshless methods require only discrete nodes constructed on domain and boundary. Finally, the parameters that influence the performance of the proposed method are assessed through several numerical examples. The results are presented for illustrating the accuracy and efficacy of the proposed numerical models.