A hybrid Lagrangian-Eulerian particle finite element method for free-surface and fluid-structure interaction problems

The dynamics of fluid flows with free surfaces and interacting with highly deformable structures is a complex problem, attracting considerable attention. The Particle Finite Element Method (PFEM) is one of the various numerical methods recently proposed in the literature to simulate this type of problems. It is a mesh-based Lagrangian approach, particularly suited for problems with fast changes in the domain topology, since the fluid boundaries and the Fluid-Structure Interaction (FSI) interface are naturally tracked by the position of the mesh nodes. However, when nonhomogeneous boundary conditions are imposed on velocities or when there are regions where the topology varies moderately, for example, in confined portions of the fluid domain characterized by fixed boundaries, an Eulerian formulation turns out to be more convenient. To exploit the advantages of both formulations, an adaptive hybrid Lagrangian-Eulerian approach is presented in this work. According to the proposed method, nodes on the fluid free-surface and on the FSI interface are treated as Lagrangian, while the remaining nodes can be either Eulerian or Lagrangian. Furthermore, to increase the efficiency of the method, an algorithm to automatically detect runtime the transition zone between the two kinematic descriptions is devised. To validate the proposed approach, several numerical examples are developed and their results are compared to those available in the literature.

Automated summary

The dynamics of fluid flows interacting with highly deformable structures is a complex problem. The Particle Finite Element Method (PFEM) is a mesh-based Lagrangian approach that can track fluid boundaries and fluid-structure interaction interface. However, for problems with nonhomogeneous boundary conditions or moderate changes in topology, an Eulerian formulation is more suitable. This work presents an adaptive hybrid Lagrangian-Eulerian approach that combines the advantages of both formulations. Numerical examples are used to validate the proposed method.