[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82355-en":3,"doc-seo-82355-105":31,"detail-sidebar-cat-0-en-105":93},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},82355,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Topology Preserving Mesh Adaptation for Sharp Interface Multiphase PFEM","This paper presents a robust fully Lagrangian framework using the Particle Finite Element Method (PFEM) to simulate multiphase flows with any number of immiscible phases. It targets common interface-tracking issues such as numerical diffusion and mesh-driven premature topological changes. A dynamic mesh adaptation strategy preserves sharp geometric interfaces without classical constrained triangulation by embedding interface segments in a Delaunay triangulation. The method separates interface physics from grid size to enable accurate sub-grid topological transitions, validated on benchmarks including a 16-phase Rayleigh–Taylor case.","arXiv :2607 .09446v 1 [ cs .CE] 10 Jul 2026  \nTopology-Preserving Mesh Adaptation for Sharp-Interface Multiphase PFEM  \nFélix Ruyffelaerea,∗, Michel Henrya , Jonathan Lambrechtsa , Jean-François Remaclea  \na UCLouvain - iMMC, Avenue Georges Lemaître 4, 1348 Louvain-la-Neuve, Belgium  \nAbstract  \nThis 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.  \nKeywords: Particle Finite Element Method (PFEM), Multiphase flows, Lagrangian tracking, Mesh adaptation, Interface conformity  \n1. Introduction  \nImmiscible multiphase flows are ubiquitous in both natural phenomena and industrial engineering applications. From environmental processes such as wave breaking and atmospheric droplet dynamics to advanced industrial applications, such as chemical bubble column reactors, microfluidics, and metallurgical casting, the interaction between distinct fluid phases governs the macroscale behavior of the system. Accurate numerical simulation of these processes is of paramount importance for the optimization of industrial designs, risk assessment, and predictive modeling of complex fluidstructure systems. Consequently, developing robust computational frameworks capable of tracking and resolving these multi-fluid interactions remains a critical focus of contemporary research in computational fluid dynamics.  \nDespite decades of methodological advancements, the high-fidelity simulation of immiscible multiphase flows presents severe mathematical and computational challenges. Chief among these is the distinct multi-scale disparity characterizing the flow; macroscale convective transport often relies heavily on localized, microscopic interfacial phenomena. Furthermore, fluid interfaces often experience extreme deformations and complex topological bifurcations such as merging, pinching, and droplet atomization [1] . Capturing these transitions accurately is highly difficult because the  \n∗ Corresponding author [Email address:](Email address: felix.ruyffelaere@uclouvain.be)[ felix.ruyffelaere@uclouvain.be](Email address: felix.ruyffelaere@uclouvain.be) (Félix Ruyffelaere)  \nunderlying physics at the interface is not fully encapsulated by the standard bulk Navier-Stokes equations alone [2] . Interfacial mechanics requires the precise evaluation of surface tension forces, which are highly sensitive to local geometric curvature. At the macroscopic scale, these forces manifest as sharp jump discontinuities in the pressure and velocity gradient fields. Crucially, the exact physical mechanisms governing topological transitions remain an open area of research, meaning numerical models must be capable of handling changing boundaries without introducing non-physical numerical artifacts.  \nHistorically, Eulerian formulations have served as the dominant paradigm for fluid simulations. In these frameworks, the governing equations are solve","cbCaibVYM3kMnLji","https://ap.wps.com/l/cbCaibVYM3kMnLji","pdf",15800839,6,1,28,"English","en",105,"# Abstract\n# Introduction\n## Background and challenges in immiscible multiphase flow simulation\n## Limitations of Eulerian interface methods (VOF, Level-Set, phase-field)\n## Motivation for Lagrangian approaches and mesh-handling challenges","[{\"question\":\"What problem does the framework address in sharp-interface multiphase simulations?\",\"answer\":\"It addresses numerical diffusion and mesh resolution forcing premature topological changes in interface-tracking methods, which can distort the physical evolution of immiscible phases.\"},{\"question\":\"How does the proposed method preserve sharp geometric interfaces during mesh adaptation?\",\"answer\":\"It assigns a node-empty disk to each discretized interface segment so the edge remains part of the Delaunay triangulation, enabling dynamic adaptation while maintaining sharp geometry.\"},{\"question\":\"How is topological change handled independently of the user-defined mesh size?\",\"answer\":\"The approach decouples interface physics from grid size, allowing sub-grid physical models to govern topological changes so the resulting transitions are not dictated by the mesh resolution.\"}]","Topology Preserving Mesh Adaptation for Sharp Interface Multiphase PFEM | 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problem does the framework address in sharp-interface multiphase simulations?","Question",{"text":77,"@type":78},"It addresses numerical diffusion and mesh resolution forcing premature topological changes in interface-tracking methods, which can distort the physical evolution of immiscible phases.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"How does the proposed method preserve sharp geometric interfaces during mesh adaptation?",{"text":82,"@type":78},"It assigns a node-empty disk to each discretized interface segment so the edge remains part of the Delaunay triangulation, enabling dynamic adaptation while maintaining sharp geometry.",{"name":84,"@type":75,"acceptedAnswer":85},"How is topological change handled independently of the user-defined mesh size?",{"text":86,"@type":78},"The approach decouples interface physics from grid size, allowing sub-grid physical models to govern topological changes so the resulting transitions are not dictated by the mesh 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