Partitioned Coupling for Structural Acoustics

Abstract

We expand the second-order fluid–structure coupling scheme of Farhat et al. (1998, “Load and Motion Transfer Algorithms for 19 Fluid/Structure Interaction Problems With Non-Matching Discrete Interfaces: Momentum and Energy Conservation, Optimal Discretization and Application to Aeroelasticity,” Comput. Methods Appl. Mech. Eng., 157(1–2), pp. 95–114; 2006, “Provably Second-Order Time-Accurate Loosely-Coupled Solution Algorithms for Transient Nonlinear Computational Aeroelasticity,” Comput. Methods Appl. Mech. Eng., 195(17), pp. 1973–2001) to structural acoustics. The staggered structural acoustics solution method is demonstrated to be second-order accurate in time, and numerical results are compared to a monolithically coupled system. The partitioned coupling method is implemented in the Sierra Mechanics software suite, allowing for the loose coupling of time domain acoustics in sierra/sd to structural dynamics (sierra/sd) or solid mechanics (sierra/sm). The coupling is demonstrated to work for nonconforming meshes. Results are verified for a one-dimensional piston, and the staggered and monolithic results are compared to an exact solution. Huang, H. (1969, “Transient Interaction of Plane Acoustic Waves With a Spherical Elastic Shell,” J. Acoust. Soc. Am., 45(3), pp. 661–670) sphere scattering problem with a spherically spreading acoustic load demonstrates parallel capability on a complex problem. Our numerical results compare well for a bronze plate submerged in water and sinusoidally excited (Fahnline and Shepherd, 2017, “Transient Finite Element/Equivalent Sources Using Direct Coupling and Treating the Acoustic Coupling Matrix as Sparse,” J. Acoust. Soc. Am., 142(2), pp. 1011–1024).

Development, verification, and validation of comprehensive acoustic fluid‐structure interaction capabilities in an open‐source computational platform

“…where Γ 𝑠𝑓 is the structural-acoustic interface. The continuity conditions are applied in a weak sense in our finite element implementation, [20,24,25] as illustrated in Figure 1. Specifically, the acceleration from the structural finite element nodes on the FSI interface, Γ 𝑠𝑓 , are converted to an acoustic pressure flux using Equation (1) and applied as a Neumann boundary condition in Equation (7) to the faces of the acoustic elements on Γ 𝑠𝑓 .…”

“…Assuming that the fluid and structure meshes are always attached, continuity of displacement (or acceleration) and traction is enforced along the interface between the fluid and the structure through the equations [ 1,36,37 ] : $$\begin{eqnarray} \frac{\partial ^2\mathbf {u}_s}{\partial t^2} &=& \frac{\partial ^2\mathbf {u}_f}{\partial t^2}, \quad \text{on}\quad \Gamma _{sf}\nonumber\\ \pmb {\sigma }_s\cdot \mathbf {n}&=&-p\mathbf {n}, \quad \text{on}\quad \Gamma _{sf} \end{eqnarray}$$where $$\Gamma _{sf}$$ is the structural‐acoustic interface. The continuity conditions are applied in a weak sense in our finite element implementation, [ 20,24,25 ] as illustrated in Figure 1. Specifically, the acceleration from the structural finite element nodes on the FSI interface, $$\Gamma _{sf}$$, are converted to an acoustic pressure flux using Equation () and applied as a Neumann boundary condition in Equation () to the faces of the acoustic elements on $$\Gamma _{sf}$$.…”

“…[21][22][23] There have also been V&V studies of acoustic FSI for both non-seismic and seismic applications. For non-seismic applications, Bunting et al [24] and Bunting and Miller [25] present V&V of acoustic FSI. For seismic applications, Rawat et al [26] and Rawat et al [27] verified and validated the wave heights from acoustic FSI for both cylindrical and rectangular tanks with numerical and experimental results from Chen et al [28] under uni-directional shaking.…”

“…For non‐seismic applications, Bunting et al. [ 24 ] and Bunting and Miller [ 25 ] present V&V of acoustic FSI. For seismic applications, Rawat et al.…”

Implicit coupling methods for nonlinear interactions between a large‐deformable hyperelastic solid and a viscous acoustic fluid of infinite extent

“…The partitioned method preserves the modularity of existing codes so that different numerical methods can be adopted for the acoustic fluid and the solid. 31,32 In addition, partitioned solution strategies range from a loose coupling procedure to strong coupling algorithms. The partitioned loose coupling strategy is very efficient since it requires no sub-iterations within each time step.…”