SUMMARYEmbedded boundary methods for CFD (computational fluid dynamics) simplify a number of issues. These range from meshing the fluid domain, to designing and implementing Eulerian-based algorithms for fluidstructure applications featuring large structural motions and/or deformations. Unfortunately, embedded boundary methods also complicate other issues such as the treatment of the wall boundary conditions in general, and fluid-structure transmission conditions in particular. This paper focuses on this aspect of the problem in the context of compressible flows, the finite volume method for the fluid, and the finite element method for the structure. First, it presents a numerical method for treating simultaneously the fluid pressure and velocity conditions on static and dynamic embedded interfaces. This method is based on the exact solution of local, one-dimensional, fluid-structure Riemann problems. Next, it describes two consistent and conservative approaches for computing the flow-induced loads on rigid and flexible embedded structures. The first approach reconstructs the interfaces within the CFD solver. The second one represents them as zero level sets, and works instead with surrogate fluid/structure interfaces. For example, the surrogate interfaces obtained simply by joining contiguous segments of the boundary surfaces of the fluid control volumes that are the closest to the zero level sets are explored in this work. All numerical algorithms presented in this paper are applicable with any embedding CFD mesh, whether it is structured or unstructured. Their performance is illustrated by their application to the solution of three-dimensional fluid-structure interaction problems associated with the fields of aeronautics and underwater implosion.

SUMMARYAn explicit-explicit staggered time-integration algorithm and an implicit-explicit counterpart are presented for the solution of non-linear transient fluid-structure interaction problems in the Arbitrary LagrangianEulerian (ALE) setting. In the explicit-explicit case where the usually desirable simultaneous updating of the fluid and structural states is both natural and trivial, staggering is shown to improve numerical stability. Using rigorous ALE extensions of the two-stage explicit Runge-Kutta and three-point backward difference methods for the fluid, and in both cases the explicit central difference scheme for the structure, secondorder time-accuracy is achieved for the coupled explicit-explicit and implicit-explicit fluid-structure time-integration methods, respectively, via suitable predictors and careful stagings of the computational steps. The robustness of both methods and their proven second-order time-accuracy are verified for sample application problems. Their potential for the solution of highly non-linear fluid-structure interaction problems is demonstrated and validated with the simulation of the dynamic collapse of a cylindrical shell submerged in water. The obtained numerical results demonstrate that, even for fluid-structure applications with strong added mass effects, a carefully designed staggered and subiteration-free time-integrator can achieve numerical stability and robustness with respect to the slenderness of the structure, as long as the fluid is justifiably modeled as a compressible medium.

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