Modeling 2D transient heat conduction problems by the numerical manifold method on Wachspress polygonal elements

Abstract

• The numerical manifold method is further developed to solve 2D transient heat conduction problems. • The Wachspress polygonal element is extended to thermal analysis. • Regular hexagonal mathematical elements are adopted in numerical examples. • Good agreement between our results and existing solutions is achieved. • The advantages of the NMM in discretization and accuracy are demonstrated. Due to the use of dual cover systems, i.e., the mathematical cover and the physical cover, the numerical manifold method (NMM) is able to solve physical problems with boundary-inconsistent meshes. Meanwhile, n -gons ( n >4) are very impressive, due to their greater flexibility in discretization, less sensitivity to volumetric and shear locking, and better suitability for complex microstructures simulation. In this paper, the NMM, combined with Wachspress-type hexagonal elements, is developed to solve 2D transient heat conduction problems. Based on the governing equations, the NMM temperature approximation and the modified variational principle, the NMM discrete formulations are deduced. The solution strategy to time-dependent global equations and the spatial integration scheme are presented. The advantages of the proposed approach in both discretization and accuracy are demonstrated through several typical examples with increasing complexity. The extension of polygonal elements in unsteady thermal analysis within the NMM is realized.