The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-017-1382-7The present paper explores the solution of a heat conduction problem considering discontinuities embedded within the mesh and aligned at arbitrary angles with respect to the mesh edges. Three alternative approaches are proposed as solutions to the problem. The difference between these approaches compared to alternatives, such as the eXtended Finite Element Method (X-FEM), is that the current proposal attempts to preserve the global matrix graph in order to improve performance. The first two alternatives comprise an enrichment of the Finite Element (FE) space obtained through the addition of some new local degrees of freedom to allow capturing discontinuities within the element. The new degrees of freedom are statically condensed prior to assembly, so that the graph of the final system is not changed. The third approach is based on the use of modified FE-shape functions that substitute the standard ones on the cut elements. The imposition of both Neumann and Dirichlet boundary conditions is considered at the embedded interface. The results of all the proposed methods are then compared with a reference solution obtained using the standard FE on a mesh containing the actual discontinuity.Peer ReviewedPostprint (author's final draft

Potential flow solvers represent an appealing alternative for the simulation of non-viscous subsonic flows. In order to deliver accurate results, such techniques require prescribing explicitly the so called Kutta condition, as well as adding a special treatment on the "wake" of the body. The wake is traditionally modelled by introducing a gap in the CFD mesh, which requires an often laborious meshing work. The novelty of the proposed work is to embed the wake within the CFD domain. The approach has obvious advantages in the context of aeroelastic optimization, where the position of the wake may change due to evolutionary steps of the geometry. This work presents a simple, yet effective, method for the imposition of the embedded wake boundary condition. The presented method preserves the possibility of employing iterative techniques in the solution of the linear problems which stem out of the discretization. Validation and verification of the solver are performed for a NACA 0012 airfoil.