Transient heat conduction modeling in continuous and discontinuous anisotropic materials with the numerical manifold method

Abstract

Transient heat conduction is a common problem in engineering. However, related studies in anisotropic materials remain relatively scarce for their complexity, compared with isotropic ones. Benefiting from the use of the two cover systems, i.e., the mathematical cover and the physical cover, the numerical manifold method (NMM) provides a unified framework for both continuous and discontinuous analyses. Herein, the NMM is applied to solve transient heat conduction problems with anisotropic materials for continuous and discontinuous cases. Firstly, the fundamental formulas for anisotropic heat conduction are displayed. Then, the NMM approximations for heat conduction in continuous and discontinuous situations are given, and the discrete formulations are derived based on the Galerkin-form weighted residual method and solved by the backward difference scheme. Finally, typical numerical examples are conducted with non-conforming mathematical covers, and the results show that the proposed method can tackle both continuous and discontinuous unsteady anisotropic heat conduction problems with high accuracy and convenience.