Unified fractional step method for Lagrangian analysis of quasi‐incompressible fluid and nonlinear structure interaction using the PFEM

Abstract

Summary The fractional step method (FSM) is an efficient solution technique for the particle finite element method, a Lagrangian‐based approach to simulate fluid–structure interaction (FSI). Despite various refinements, the applicability of the FSM has been limited to low viscosity flow and FSI simulations with a small number of equations along the fluid–structure interface. To overcome these limitations, while incorporating nonlinear response in the structural domain, an FSM that unifies structural and fluid response in the discrete governing equations is developed using the quasi‐incompressible formulation. With this approach, fluid and structural particles do not need to be treated separately, and both domains are unified in the same system of equations. Thus, the equations along the fluid–structure interface do not need to be segregated from the fluid and structural domains. Numerical examples compare the unified FSM with the non‐unified FSM and show that the computational cost of the proposed method overcomes the slow convergence of the non‐unified FSM for high values of viscosity. As opposed to the non‐unified FSM, the number of iterations required for convergence with the unified FSM becomes independent of viscosity and time step, and the simulation run time does not depend on the size of the FSI interface. Copyright © 2016 John Wiley & Sons, Ltd.

A State of the Art Review of the Particle Finite Element Method (PFEM)

“…A matrixfree technique is used for the solution of such a linear system. In [138][139][140], ill-conditioning issues of the monolithic formulation had been overcome by applying a fractional step approach to the linear system, segregating pressures and velocities unknowns into smaller systems of equations. There also exist several partitioned PFEM approaches for FSI problems.…”

Fast fluid–structure interaction simulations using a displacement-based finite element model equipped with an explicit streamline integration prediction

“…Mass conservation equation used here corresponds to a commonly used quasi-incompressible approximation. The advantages of using the quasiincompressible rather than fully incompressible fluid formulation for the implementation of tightly coupled FSI solvers have been numerously demonstrated [25], [10], [7], [26], [3], [1], [6].…”

“…Since in Lagrangian approaches the computational mesh follows the fluid movement, tracking the moving boundaries does not require any additional techniques being an intrinsic feature of the model. Lagrangian fluid and fluid-structure interaction models have been developed both in the Finite Element Method (FEM) [1], [2], [3], [4], [5], [6], [7] and the Smooth Particle Hydrodynamics (SPH) contexts [8], [9], [10], [11].…”

An explicit–implicit finite element model for the numerical solution of incompressible Navier–Stokes equations on moving grids

“…Majority of the existing Lagrangian finite element-based fluid models are relying on fully implicit time integration schemes [19,16,8,20,11,21,22,23].…”