A mixed Lagrangian-Eulerian formulation for free-surface 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 a lot of attention from engineering communities. The presence of free surfaces and fast evolving interfaces further complicates the FSI problem, making it more challenging to find efficient tools for its numerical solution. Traditionally, Eulerian or Arbitrary Lagrangian-Eulerian (ALE) approaches have been preferred for the solution of FSI problems. However, recently proposed mesh-based Lagrangian approaches have also been proven to be very efficient, especially in the presence of free surfaces and FSI interfaces. Nonetheless, in a mesh-based Lagrangian approach, the position of mesh nodes is updated according to fluid velocities, causing excessive mesh distortion that requires continuous remeshing. To address this issue, the Particle Finite Element Method (PFEM) was introduced as an innovative numerical technique that exploits the Lagrangian approach by coupling an efficient finite element solver with a runtime remeshing algorithm. The PFEM was initially introduced for solving free surface flows but has also demonstrated the ability to simulate FSI problems and many other engineering problems. However, in some specific problems, the Lagrangian approach may not be particularly suitable, and an Eulerian description may be more convenient. In this work, we propose a mixed Lagrangian-Eulerian kinematic model for PFEM. The proposed technique divides the fluid domains into Eulerian and Lagrangian regions to fully exploit their advantages. The Lagrangian approach is used close to free surfaces and fluid-structure interfaces, whereas the Eulerian approach is adopted elsewhere. The proposed method is extended to FSI problems by introducing a remeshing region enclosing the structure. Inside this region, nodes are treated as Lagrangian to facilitate interface tracking, while the remaining nodes are set to be Eulerian. During the analysis, the position and space extension of the remeshing region is updated following the movements of the solid body.