A differential variational approach for handling fluid-solid interaction problems via smoothed particle hydrodynamics

The fluid-solid interaction (FSI) problem is customarily solved by starting with the fluid dynamics component. One chooses an established computational fluid dynamics (CFD) method and subsequently embeds the solid phase dynamics within the CFD solution leading to either a monolithic or a staggered/co-simulated solution. The approach discussed here takes the opposite tack. We start with a differential variational framework to handle the solid phase; i.e., the multi-body dynamics problem in the presence of contact, friction, and bilateral kinematic constraints. The dynamics of the fluid phase, which is captured via smoothed particle hydrodynamics (SPH), is subsequently embedded into this framework in which the incompressibility attribute of the flow is enforced via kinematic constraint equations that involve SPH particles. The resulting monolithic FSI solution methodology relies on a half-implicit symplectic time integration method that uses a matrix-free iterative approach to solve a cone constrained quadratic optimization problem at each time step. This problem yields the contact forces, friction forces, boundary condition Lagrange multipliers, fluid-solid coupling terms, and bilateral constraint Lagrange multipliers. The solution of the optimization problem represents the computationally taxing component of the method. Large integration time steps, tight enforcement of incompressibility, a unified approach for handling the fluid and solid phases, and linear scaling are listed as the attractive attributes of the proposed method. The numerical experiments reported include three validation studies (incompressibility, dam break, and sloshing), a scaling analysis, and a tracked vehicle fording simulation.