COUPLED 2025

PFEM-VEM-FEM Coupling for the Simulation of Fast-Evolving Fluid-Structure Interaction Problems

  • Cremonesi, Massimiliano (Politecnico di Milano)
  • Fu, Cheng (Politecnico di Milano)
  • Perego, Umberto (Politecnico di Milano)

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The interaction between fluids and highly deformable structures (FSI), is an interesting and complex problem that attracts significant attention from engineering community. The presence of free surfaces and rapidly evolving interfaces further complicates the FSI problem, making it more challenging to develop efficient numerical tools. Traditionally, Eulerian or Arbitrary Lagrangian-Eulerian (ALE) approaches have been preferred for the solution of FSI problems. However, recent developments in mesh-based Lagrangian approaches have proven to be highly effective, particularly in scenarios involving free surfaces and evolving FSI interfaces. In a mesh-based Lagrangian approach, the mesh nodes are updated according to fluid velocities, which can lead to excessive mesh distortion and necessitate continuous remeshing. To address this issue, the Particle Finite Element Method (PFEM) was introduced as an innovative numerical technique combining the Lagrangian approach with an efficient finite element solver and a dynamic remeshing algorithm. Initially developed for simulating free surface flows, PFEM has also demonstrated its capability in solving FSI problems and a variety of other complex engineering problems. To mitigate excessive mesh distortion within the PFEM framework, once the current mesh becomes excessively distorted, a new one is created through a Delaunay tessellation. However, the 3D Delaunay tessellation does not always produce elements with optimal geometric properties, resulting in nearly zero-volume elements (slivers). Even a single sliver can significantly impact explicit analyses by drastically reducing the stable time step size. To mitigate this issue, poorly shaped elements are merged with neighboring elements to form Virtual Elements with arbitrary shapes and characterized by larger stable time steps. The proposed method is extended to FSI problems by coupling PFEM with a standard FEM solver for the solid part exploiting a GC Domain Decomposition approach [2].The fluid and solid domains are solved independently, as if there were no interactions, and are then coupled at the interface using a Lagrange multiplier technique. The proposed approach has been validated with large scale 3D tests showing also also possible applications to engineering problems with fast dynamics and a high degree of non-linearity.