Numerical verification of a nonlocal discrete model for anisotropic heat conduction problems

This paper presents the numerical study of a recently proposed nonlocal discrete model for anisotropic heat conduction problems. Both transient and steady-state heat conduction problems are studied. The solution schemes and applications of the temperature and flux boundary conditions are discussed in detail. Various benchmark problems are employed to demonstrate the convergence characteristic and the prediction accuracy of the proposed model. The proposed model is then applied to study the heat conduction in a bi-continuous composite microstructure. It is observed that the proposed model has an expected linear convergence rate and can accurately predict the solution with respect to finite element results. As demonstrated using the bi-continuous microstructure, the proposed model offers significant convenience to image-based modeling and simulation by directly take the digitized material voxels as discrete material particles without generating quality mesh.