A Lagrangian-Lagrangian Framework for the Simulation of Fluid-Solid Interaction Problems with Rigid and Flexible Components

This work is concerned with formulating and validating a Lagrangian-Lagrangian (LL) 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. The motion of flexible objects and arbitrarily-shaped rigid bodies are modeled using an Absolute Nodal Coordinate Formulation (ANCF) and a classical 3D rigid body dynamics framework, respectively. 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 used to impose no-slip and impenetrability conditions. The BCE markers are distributed in a narrow layer on and below the surface of solid objects as well as confining walls. The solid-solid interaction is known to have a crucial effect on the small-scale behavior of fluid-solid mixtures. The dry encounter of solid surfaces is resolved herein through a penalty based approach. A lubrication force model is proposed to accommodate the wet interaction of the arbitrary 3D geometries. 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 the rigid or flexible body motion. The proposed methodology is implemented in a multi-threaded, multi-scale high performance computing approach using Graphics Processing Unit (GPU) and is used to validate several problems involving two- and three-dimensional (2D, 3D) pipe flow of dilute suspensions of macroscopic neutrally buoyant rigid bodies at flow regimes with Reynolds numbers (Re) between 0.1 and 1400. Performance and scaling analysis are provided for simulations scenarios that include one or multiple phases with up to tens of thousands of colloidal rigid and flexible objects. Furthermore, several problems including flow cytometry using microfluidic techniques, flow within porous media, and vibration analysis of immersed flexible objects were approached using the proposed methodology. The software implementation of the algorithm, called Chrono::Fluid, is available as an open-source.