A cut-cell finite volume – finite element coupling approach for fluid–structure interaction in compressible flow

Abstract

We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables subcell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface. The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. We validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid-structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large * Corresponding author.

Constrained moving least‐squares immersed boundary method for fluid‐structure interaction analysis

“…The instantaneous density and pressure contours computed using a uniform 800 × 160 grid at t = 0.14 s and 0.255 s are presented in Figures 19 and 20, respectively. The results show that the solid positions and the shock patterns determined by the present method agree well with those reported by Monasse et al 31 and Pasquariello et al 32 A strong vortex below the rigid cylinder exists throughout the entire cylinder trajectory, which is also reported by Monasse et al 31 and Pasquariello et al 32 This vortex is probably associated with a Kelvin-Helmholtz instability of the contact discontinuity present under the cylinder.…”

“…The moving body problem studied by Monasse et al 31 The computed results for the horizontal and the vertical positions of the mass center of the cylinder at t = 0.255 s are compared in Figure 18 with those of Monasse et al 31 and Pasquariello et al 32 Different grid resolutions of 1/dx = 1/dy = 400, 600, and 800 are used in the computation. The presently computed final position of the cylinder is in reasonable agreement with those of the 2 reference solutions.…”

A positive-definite cut-cell method for strong two-way coupling between fluids and deformable bodies

“…While various avors of immersed boundary and cut-cell methodologies are common, we are not aware of any method that o ers the speci c advantages provided by the present work. As an example, Pasquariello et al [2016] use a cut-cell nite di erence/volume strategy in a manner broadly similar to our work and that of Ng et al [2009]. In contrast to our work though, they consider compressible ow, handle the boundary interactions via a mortar method based on explicit Lagrange multiplier constraints, and employ a weak/partitioned coupling strategy.…”

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid-Structure Interaction

“…The interaction of aerodynamic, inertial and elastic forces can cause a phenomenon known as flutter, which is caused by an aeroelastic instability. The simulation setup was chosen in accordance with Dowell 42 and Vito et al 43 For this setup, the critical Mach number where the instability occurs is M crit = 2.0. For larger Mach numbers a growth of the oscillations is expected.…”