Stabilized Nitsche-Type CIP/GP CutFEM for Two-Phase Flow Applications

Himali Gammanpila, Eugenio Aulisa () and Andrea Chierici
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Himali Gammanpila: Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, KY 40475, USA
Eugenio Aulisa: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA
Andrea Chierici: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA

Mathematics, 2025, vol. 13, issue 17, 1-31

Abstract: This work presents a stabilized Nitsche-type Cut Finite Element Method (CutFEM) for simulating two-phase flows with complex interfaces. The method addresses the challenges of capturing discontinuities in material properties and governing equations that arise from implicitly defined interfaces. By employing a Continuous Interior Penalty (CIP) method, Nitsche’s method for weak interface coupling, and Ghost Penalty (GP) terms for stability, the formulation enables an accurate representation of abrupt changes in physical properties across cut elements. A stability analysis and a priori error estimation, utilizing Oseen’s formulation, demonstrate the method’s robustness. At the same time, a numerical convergence study incorporating adaptivity and a best-fit quadratic level-set interpolation validates its accuracy. Finally, the method’s efficacy in mitigating spurious currents is confirmed through the Spurious Current Test, demonstrating its potential for reliable simulation of multi-phase flow phenomena.

Keywords: cut finite element method (CutFEM); two-phase flow; complex interfaces; ghost penalty; continuous interior penalty; adaptive mesh (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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