A Lagrangian-Lagrangian framework for the simulation of rigid and deformable bodies in fluid

We present a Lagrangian-Lagrangian approach for the simulation of fully resolved Fluid Solid/Structure Interaction (FSI) problems. In the proposed approach, the method of Smoothed Particle Hydrodynamics (SPH) is used to simulate the fluid dynamics in a Lagrangian framework. The solid phase is a general multibody dynamics system composed of a collection of interacting rigid and deformable objects. While the motion of arbitrarily shaped rigid objects is approached in a classical 3D rigid body dynamics framework, the Absolute Nodal Coordinate Formulation (ANCF) is used to model the deformable components, thus enabling the investigation of compliant elements that experience large deformations with entangling and self-contact. The dynamics of the two phases, fluid and solid, are coupled with the help of Lagrangian markers, referred to as Boundary Condition Enforcing (BCE) markers which are used to impose no-slip and impenetrability conditions. Such BCE markers are associated both with the solid suspended particles and with any confining boundary walls and are distributed in a narrow layer on and below the surface of solid objects. The ensuing fluid-solid interaction forces are mapped into generalized forces on the rigid and flexible bodies and subsequently used to update the dynamics of the solid objects according to rigid body motion or ANCF method. The robustness and performance of the simulation algorithm is demonstrated through several numerical simulation studies.