arXiv:2611.13921v1 Announce Type: cross Abstract: We present a marker-based X-Mesh framework for incompressible N-phase flow simulations with sharp, explicitly tracked interfaces. The interface is represented by Lagrangian marker chains, while the computational mesh is deformed so that selected mesh edges conform to the tracked geometry without changing mesh connectivity. This combination preserves the advantages of body-fitted finite element discretizations while allowing highly distorted and nearly degenerated elements to capture fine interfacial features on relatively coarse meshes without requiring mesh refinement. The arbitrary Lagrangian-Eulerian (ALE) finite element solver uses a pressure field that is continuous within each phase and discontinuous across the fitted interface. Surface tension is introduced through a variational membrane, so the pressure jump is resolved without prescribing a curvature-dependent correction; a Young wall energy provides the corresponding treatment of fluid-fluid-solid triple points. Topological changes are handled geometrically from the marker representation. Numerical experiments illustrate the ability of the approach to transport complex interfaces and to control topology changes through marker-based feature-size criteria.