An improved enrichment method for weak discontinuities for thermal problems

Published in Int. J. of Num. Meths. for Heat and Fluid Flow Vol. 27 (8), pp. 1748-1764, 2017
doi:10.1108/HFF-06-2016-0219

Abstract

Purpose The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities.

Design/methodology/approach The enrichment is introduced in the elements cut by the materials interface by means of adding additional shape functions. The weak form of the problem is obtained using Galerkin approach and subsequently integrating the diffusion term by parts. To enforce the continuity of the fluxes in the “cut” elements, a contour integral must be added. These contour integrals named here the “inter-elemental heat fluxes” are usually neglected in the existing enrichment approaches. The proposed approach takes these fluxes into account.

Findings It has been shown that the inter-elemental heat fluxes cannot be generally neglected and must be included. The corresponding method can be easily implemented in any existing finite element method (FEM) code, as the new degrees of freedom corresponding to the enrichment are local to the elements. This allows for their static condensation, thus not affecting the size and structure of the global system of governing equations. The resulting elements have exactly the same number of unknowns as the non-enriched finite element (FE).

Originality/value It is the first work where the necessity of including inter-elemental heat fluxes has been demonstrated. Moreover, numerical tests solved have proven the importance of these findings. It has been shown that the proposed enrichment leads to an improved accuracy in comparison with the former approaches where inter-elemental heat fluxes were neglected.