X-MESH and PFEM2 Coupling for the Simulation of Flows Around Moving Rigid Bodies

Abstract

The numerical simulation of fluid flows involving moving interfaces is a major challenge in computational mechanics. Such problems arise in a wide range of applications, including free-surface flows, fluid–structure interaction (FSI) and multiphase systems. Accurately capturing the evolution of these interfaces while maintaining computational efficiency remains a key difficulty. To address this challenge, this work investigates the coupling between the X-MESH methodology and a PFEM2 solver in the special case of a moving rigid body in two dimensions. The main goal of this work was to couple an X-MESH code with a Particle Finite Element Method second generation (PFEM2) solver. The fluid solver consists of a parallel MPI-based C++ code, called Par2FEM, built on top of the PETSc library. The solid body is represented implicitly through a level-set function and the X-MESH methodology is used to locally adapt the mesh near the interface, ensuring a geometrically conforming representation while preserving the fixed background mesh required by PFEM2. The coupling required significant modifications on both sides. On the X-MESH side, improvements were made to the node relocation strategy, including a node-switching mechanism when an edge shrinks below half its original length and an improved handling of shared nodes between MPI processes in complex interface configurations. Limitation of the X-MESH code are also discussed. On the PFEM2 side, the algorithm was extended to incorporate dynamic boundary condition updates with system assembly, force extractor adaptations, particle-to-mesh projection corrections. The methodology was validated on two benchmark cases. First, a fixed cylinder at Reynolds number 100 showed good agreement with literature results in terms of drag coefficient, lift amplitude. Second, an inline oscillating cylinder was simulated and compared against reference data, showing satisfying agreement only for the inline force. A scalability analysis revealed a suboptimal parallel efficiency, mainly attributed to the resolution of the linear system on a coarse mesh.