An improved enrichment method for weak discontinuities for thermal problems

Julio Marti (Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain and Department of Civil and Environmental Engineering, Universitad Politècnica de Catalunya (UPC), Barcelona, Spain)
Ernesto Ortega (Department of Computer Science, Centro de Investigacion en Matematicas Guanajuato, Guanajuato, Mexico)
Sergio Idelsohn (Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain and Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 7 August 2017

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.

Keywords

Citation

Julio Marti, Ernesto Ortega and Sergio Idelsohn (2017) "An improved enrichment method for weak discontinuities for thermal problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 8, pp. 1748-1764

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DOI

: https://doi.org/10.1108/HFF-06-2016-0219

Publisher

:

Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited

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