XFEM+: Una modificación de XFEM para mejorar la precisión de los flujos locales en problemas de difusión con conductividades muy distintas

Abstract

When applied to diffusion problems in a multiphase setup, the popular XFEM strategy suffers of an inaccurate representation of the local fluxes in the vicinity of the interphase. The XFEM enrichment improves the global quality of the solution but it is not enforcing any local feature to the fluxes. Thus, the resulting numerical fluxes in the vicinity of the interphase are not realistic. This paper introduces an additional restriction to the XFEM formulation aiming at properly reproducing the features of the local fluxes in the transition zone. This approach is denoted as XFEM+ and requires adding linear constrains to the XFEM algebraic system. The XFEM+ strategy is applied to several examples and the solutions obtained show a spectacular improvement with respect to the standard XFEM.

Full document