Improved fractional step method for simulating fluid‐structure interaction using the PFEM

Abstract

SUMMARYNumerical difficulties are present in the particle finite element method even though it has been shown to be a powerful and effective approach to simulating fluid-structure interaction. To overcome problems of mass loss on the free surface and the added-mass effect, an improved fractional step method (FSM) that handles addedmass terms in a mathematically exact way is developed. A further benefit is that no assumptions regarding the structural response are made in handling added-mass terms, thus it is straightforward to incorporate material nonlinearity in fluid-structure interaction (FSI) under this approach. Patch tests and comparisons with experimental data are presented in order to verify and validate the improved FSM for FSI applications. The computational cost of this approach is shown to be negligible compared with the other aspects of the FSM, particularly when the size of the structure and the fluid-structure interface is small relative to the volume of fluid.

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

“…Usually, the FSM for incompressible fluid involves three steps of velocity prediction, pressure solution, and velocity correction. However, difficulties are encountered in solving the unified system of Equation at the second step because an inversion of the matrix is required, as noted in . The inversion could be approximated, but this will lead to inaccuracy of the FSI response and violation of mass conservation.…”

“…For example, the unified FSM is able to handle high viscous fluid flow, higher‐order fluid elements that require consistent mass matrices, and nonlinear structural response in an efficient manner while also eliminating explicit tracking of the fluid–structure interface. Although the improved FSM in is also able to accommodate nonlinear structural response, the size of the FSI interface hinders the method's computational efficiency because the matrix is not fully diagonal.…”

“…There is good agreement between analytical and numerical solutions. The same problem is also solved using the non‐unified method . As shown in Figure , the non‐unified method gives similar answers as the unified method.…”

“…The proposed unified FSM and non‐unified FSM are run using viscosity μ = 10 −3 Pa‐s and time step Δ t = 10 −3 s with snap shots of the simulation shown in Figure . Flexural yielding initiates at the left end of the bottom beam, followed by yielding at the right end and middle of the beam.…”

“…However, the fluid is assumed to be inviscid or nearly inviscid, and the mass matrix is lumped in order to compute the discrete Laplacian matrix efficiently. The FSMD is limited to fluid interaction with rigid bodies because it does not consider the structural contribution to pressure. An improved FSM proposed by extends the FSMD by incorporating both structural stiffness and mass in the discrete Laplace matrix. This approach was shown to conserve mass, be numerically stable for the added‐mass effect, and able to handle arbitrary structures with material and geometric nonlinearity.…”