Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space

Abstract

In a previous paper, the authors presented an elemental enriched space to be used in a finite-element framework (EFEM) capable of reproducing kinks and jumps in an unknown function using a fixed mesh in which the jumps and kinks do not coincide with the interelement boundaries. In this previous publication, only scalar transport problems were solved (thermal problems). In the present work, these ideas are generalized to vectorial unknowns, in particular, the incompressible Navier-Stokes equations for multifluid flows presenting internal moving interfaces. The advantage of the EFEM compared with global enrichment is the significant reduction in computing time when the internal interface is moving. In the EFEM, the matrix to be solved at each time step has not only the same amount of degrees of freedom (DOFs) but also the same connectivity between the DOFs. This frozen matrix graph enormously improves the efficiency of the solver. Another characteristic of the elemental enriched space presented here is that it allows a linear variation of the jump, thus improving the convergence rate, compared with other enriched spaces that have a constant variation of the jump. Furthermore, the implementation in any existing finite-element code is extremely easy with the version presented here because the new shape functions are based on the usual finite-element method shape functions for triangles or tetrahedrals, and once the internal DOFs are statically condensed, the resulting elements have exactly the same number of unknowns as the nonenriched finite elements.