Topology-Preserving Mesh Adaptation for Sharp-Interface Multiphase PFEM

2026-07-10

AI Summary

This work addresses the challenge of numerical diffusion and premature mesh-driven topological changes in multiphase flow simulations. It proposes a fully Lagrangian framework based on the Particle Finite Element Method (PFEM), which integrates dynamic mesh adaptivity with a node-based empty circumcircle criterion to guarantee that interface edges always conform to the Delaunay triangulation. This approach preserves sharp interface geometry without imposing explicit constraints on the triangulation, effectively decoupling interfacial physics from mesh resolution and enabling independent control of topological evolution at sub-grid scales. Validated against standard multiphase benchmarks, the method achieves excellent agreement with reference solutions using significantly fewer nodes and successfully simulates a 16-phase Rayleigh–Taylor instability, demonstrating its scalability and geometric versatility.

Abstract

This paper presents a robust, fully Lagrangian framework based on the Particle Finite Element Method (PFEM) capable of simulating multiphase flows with an arbitrary number of immiscible phases. Interface-tracking methods can sometimes suffer from numerical diffusion or allow the underlying mesh resolution to prematurely dictate topological changes. To address these limitations, we introduce a dynamic mesh adaptation strategy that naturally preserves sharp geometric interfaces without relying on classical constrained triangulation. A node-empty disk is assigned to each segment of the discretized interface, ensuring that the edge is part of the Delaunay triangulation. Our approach decouples the interface physics from the grid size, allowing the integration of sub-grid physical models to properly govern topological changes independently of the user-defined mesh size. The capabilities and accuracy of the framework are validated against standard multiphase benchmarks, closely matching references while maintaining a remarkably low overall node count. We demonstrate the scalability and geometric versatility of the method, in particular with a challenging 16-phase Rayleigh-Taylor simulation.

Problem

• multiphase flow
• interface tracking
• topology preservation
• mesh adaptation
• sharp interface

Innovation

• mesh adaptation
• sharp-interface
• Particle Finite Element Method
• topology preservation
• Delaunay triangulation