A series solution based formulation for discrete thermal element method of granular materials

This work performs further study on the discrete thermal element method (DTEM) (Feng et al., J. Comput. Phys. 227, 5072–5089 (2008)) of heat conduction in particle systems involving a large number of circular particles in 2D cases. Feng proposed the DTEM based on particular solution for the Laplace equation in a circular domain with Newmann boundary condition. In this paper, another version of DTEM is proposed based on the series solution for the same boundary value problem. The evaluation of the coefficients of the resistance matrix He is a main computational issue associated with the formulation of the DTEM. In this work, another accurate and less time consuming method for calculating He is presented. The resulting equation gives a better expression for hij while in Feng’s work, this was done numerically. An important mathematical property of He is also discovered and discussed. The More Diagonally-Dominant pipe-network model is proposed to make the pipe-network model (Feng et al., Powder Technol. 193, 248–256 (2009)) more accurate. Numerical experiments are conducted to establish the solution accuracy of the proposed method.