An XFEM Formulation for Surface Tension Forces in Two-Phase Flow
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Accurate numerical modeling of surface-tension–driven two-phase flows is challenging, primarily due to spurious currents and pressure discontinuities. In this work, we propose a volumetric surface-tension formulation specifically designed to reduce spurious currents, embedded within the XFEM framework, which allows an exact representation of pressure jumps. Both the surface-tension model and the XFEM basis functions are integrated using an exact polynomial integration technique that avoids cut-cell subdivision, making the method easily extendable to three dimensions. The approach is validated on surface-tension–driven benchmarks, including relaxation to equilibrium and oscillation period computations, demonstrating reduced spurious currents together with consistency and numerical accuracy.
