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

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.