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 H_e is a main computational issue associated with the formulation of the DTEM. In this work, another accurate and less time consuming method for calculating H_e 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 H_e 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.

离散热元件方法这项工作进行进一步的研究（DTEM）（Feng等人，J。COMPUT。物理学。227热传导的粒子系统，5072-5089（2008））涉及大量二维圆形颗粒的案件。Feng提出了基于纽曼边界条件的圆域中Laplace方程的特殊解的DTEM 。本文基于相同边值问题的级数解，提出了另一种DTEM版本。电阻矩阵H _e的系数的评估是与DTEM公式相关的主要计算问题。在这项工作中，另一种计算H _e的准确而省时的方法被呈现。所得方程为hij提供了更好的表达式，而在冯的工作中，这是通过数字完成的。还发现和讨论了H _e的重要数学性质。提出的对角更主导管网络模型，使管道-网络模型（Feng等，粉末TECHNOL。193，248-256（2009））更准确。进行数值实验以建立所提出方法的求解精度。