Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping

Abstract

Summary In this study, the extended finite element method (XFEM) is applied to the two‐dimensional Laplace equation with an internal discontinuity. The real part of a complex velocity potential from potential flow theory is used to represent the enrichment function in this technique. The Joukowski mapping, which maps a circle to a line, is mainly used to obtain a solution around an airfoil in two‐dimensional potential flow; here, we extend that solution to model magnetic flux around an internal crack. The effectiveness of the proposed method is verified using numerical examples of single and multiple cracks. The L2 error norm is used to evaluate the accuracy of the proposed method in comparison with XFEM using previously proposed enrichment functions (Heaviside and analytical forms for a single crack tip). The proposed method gives better results than those of the existing XFEM in the case of a coarse mesh.