Himali Gammanpila, Texas Tech University
Authors: Himali Gammanpila , Dr. Eugenio Aulisa
2023 AWM Research Symposium
Poster Presentation

Two-phase flows are encountered in various industrial applications and natural phenomena. Since the interface is significantly thin in two-phase flow, it can be treated as a discontinuity in the flow field where localized surface tension forces act. Defining the interface implicitly means that elements may be intersected by the interface, and the aforementioned discontinuities may occur inside them. When using the finite element method (FEM) with polynomial shape functions, these discontinuities cannot be explicitly represented. Therefore, many PDE solvers employ a discontinuous function, especially in the context of fluid dynamics problems. These methods utilize discontinuous functions to distinguish different domains and ensure no extrinsic contributions are incurred when utilizing an arbitrary discontinuity. An extension of FEM utilizing discontinuous functions is CutFEM or Extended FEM (XFEM), which allows for reproducing arbitrary discontinuities inside elements by providing an enhanced shape function basis. In this study, a Nitsche-type extended variational multiscale method for two-phase flow is suggested, specifically for discontinuous pressure. To ensure a stable formulation across the entire domain, Continuous Interior Penalty (CIP) based variational multiscale terms are supported by appropriate face-oriented ghost-penalty terms. These terms are introduced to sufficiently control the enrichment value of the solution fields, thereby ensuring the stability of the formulation. The numerical analysis of the proposed CutFEM starts by providing the bilinear form that satisfies an inf-sup condition with respect to a suitable norm. The inf-sup constant is independent of how the boundary cuts the underlying mesh. Furthermore, energy-type a priori estimates are proved to be independent of the local Reynolds number.

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