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

IDELSOHN, SERGIO R.; GIMENEZ, JUAN M.; NIGRO, NORBERTO M.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

JOHN WILEY & SONS LTD

Año: 2018 vol. 86 p. 750 - 769

0271-2091

In a previous paper the authors present an elemental enriched space to beused in a finite element framework (EFEM) capable to reproduce kinks andjumps in an unknown function using a fixed mesh in which the jumps andkinks do not coincide with the inter-element boundaries. In this previous pub-lication, only scalar transport problems where solved (thermal problems). Inthe present work these ideas are generalized to vectorial unknowns, in partic-ular the incompressible Navier-Stokes equations for multi-fluid flows present-ing internal moving interfaces. The advantage of the EFEM compared withthe global enrichment is the important reduction of the computing time whenthe internal interface is moving. In the EFEM the matrix to be solved ateach time-step has, not only the same amount of degrees of freedom (DOFs)but also has always the same connectivity between the DOFs. This frozenmatrix-graph improves enormously the efficiency of the solver. Another char-acteristic of the elemental enriched space presented here is that it allows alinear variation of the jump, improving the convergence rate compared withother enriched spaces that have a constant variation of the jump. Further-more, the implementation in any existing finite element code is extremelyeasy with the version presented here because the new shape functions arebased on the usual FEM shape functions for triangles or tetrahedrals and,once statically condensed the internal DOFs, the resulting elements haveexactly the same number of unknowns as the non-enriched finite elements.