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.

SUMMARY A robust, accurate, and computationally efficient interface tracking algorithm is a key component of an embedded computational framework for the solution of fluid–structure interaction problems with complex and deformable geometries. To a large extent, the design of such an algorithm has focused on the case of a closed embedded interface and a Cartesian computational fluid dynamics grid. Here, two robust and efficient interface tracking computational algorithms capable of operating on structured as well as unstructured three‐dimensional computational fluid dynamics grids are presented. The first one is based on a projection approach, whereas the second one is based on a collision approach. The first algorithm is faster. However, it is restricted to closed interfaces and resolved enclosed volumes. The second algorithm is therefore slower. However, it can handle open shell surfaces and underresolved enclosed volumes. Both computational algorithms exploit the bounding box hierarchy technique and its parallel distributed implementation to efficiently store and retrieve the elements of the discretized embedded interface. They are illustrated, and their respective performances are assessed and contrasted, with the solution of three‐dimensional, nonlinear, dynamic fluid–structure interaction problems pertaining to aeroelastic and underwater implosion applications. Copyright © 2012 John Wiley & Sons, Ltd.

We formulate a theory of non-equilibrium statistical thermodynamics for ensembles of atoms or molecules. The theory is an application of Jayne's maximum entropy principle, which allows the statistical treatment of systems away from equilibrium. In particular, neither temperature nor atomic fractions are required to be uniform but instead are allowed to take different values from particle to particle. In addition, following the Coleman-Noll method of continuum thermodynamics we derive a dissipation inequality expressed in terms of discrete thermodynamic fluxes and forces. This discrete dissipation inequality effectively sets the structure for discrete kinetic potentials that couple the microscopic field rates to the corresponding driving forces, thus resulting in a closed set of equations governing the evolution of the system. We complement the general theory with a variational meanfield theory that provides a basis for the formulation of computationally tractable approximations. We present several validation cases, concerned with equilibrium properties of alloys, heat conduction in silicon nanowires and hydrogen desorption from palladium thin films, that demonstrate the range and scope of the method and assess its fidelity and predictiveness. These validation cases are characterized by the need or desirability to account for atomiclevel properties while simultaneously entailing time scales much longer than * Corresponding author E-mail address: ortiz@caltech.edu (M. Ortiz). September 27, 2014 those accessible to direct molecular dynamics. The ability of simple meanfield models and discrete kinetic laws to reproduce equilibrium properties and long-term behavior of complex systems is remarkable. Preprint submitted to Journal of the Mechanics and Physics of Solids

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A robust computational framework for the solution of fluid-structure interaction problems characterized by compressible flows and highly nonlinear structures undergoing pressure-induced dynamic fracture is presented. This framework is based on the finite volume method with exact Riemann solvers for the solution of multi-material problems. It couples a Eulerian, finite volume-based computational approach for solving flow problems with a Lagrangian, finite element-based computational approach for solving structural dynamics and solid mechanics problems. Most importantly, it enforces the governing fluid-structure transmission conditions by solving local, one-dimensional, fluid-structure Riemann problems at evolving structural interfaces, which are embedded in the fluid mesh. A generic, comprehensive, and yet effective approach for representing a fractured fluid-structure interface is also presented. This approach, which is applicable to several finite element-based fracture methods including inter-element fracture and remeshing techniques, is applied here to incorporate in the proposed framework two different and popular approaches for computational fracture in a seamless manner: the extended FEM and the element deletion method. Finally, the proposed embedded boundary computational framework for the solution of highly nonlinear fluid-structure interaction problems with dynamic fracture is demonstrated for one academic and three realistic applications characterized by detonations, shocks, large pressure, and density jumps across material interfaces, dynamic fracture, flow seepage through narrow cracks, and structural fragmentation. Correlations with experimental results, when available, are also reported and discussed. For all four considered applications, the relative merits of the extended FEM and element deletion method for computational fracture are also contrasted and discussed. . Multi-fluid and multi-material flows are typically characterized by the presence in well-defined regions of space of two or more fluids with different material properties. Multi-phase flows feature different phases or mixtures of fluids. For the purpose of this paper, all three labels are unified under the name 'multi-material', as this label is most suitable for describing the additional structural aspect of the aforementioned coupled problems.The development of a computational framework for the simulation of highly nonlinear, highspeed, multi-material FSI problems with dynamic fracture is a formidable challenge. It requires accounting for all possible interactions of all fluid and structural subsystems and therefore tracking all fluid-fluid and fluid-structure interfaces. It also necessitates the proper discretization of the governing flow equations across fluid-fluid interfaces involving different equations of state (EOSs) and high density jumps and fluid-structure interfaces undergoing topological changes. The development of such a computational framework also calls for the modeling of geometrical nonlinearities, material failure a...

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Partitioned procedures are appealing for solving complex fluid-structure interaction (FSI) problems, as they allow existing computational fluid dynamics (CFD) and computational structural dynamics algorithms and solvers to be combined and reused. However, for problems involving incompressible flow and strong added-mass effect (eg, heavy fluid and slender structure), partitioned procedures suffer from numerical instability, which typically requires additional subiterations between the fluid and structural solvers, hence significantly increasing the computational cost. This paper investigates the use of Robin-Neumann transmission conditions to mitigate the above instability issue. Firstly, an embedded Robin boundary method is presented in the context of projection-based incompressible CFD and finite element-based computational structural dynamics. The method utilizes operator splitting and a modified ghost fluid method to enforce the Robin transmission condition on fluid-structure interfaces embedded in structured non-body-conforming CFD grids. The method is demonstrated and verified using the Turek and Hron benchmark problem, which involves a slender beam undergoing large transient deformation in an unsteady vortex-dominated channel flow. Secondly, this paper investigates the effect of the combination parameter in the Robin transmission condition, ie, f , on numerical stability and solution accuracy. This paper presents a numerical study using the Turek and Hron benchmark problem and an analytical study using a simplified FSI model featuring an Euler-Bernoulli beam interacting with a two-dimensional incompressible inviscid flow. Both studies reveal a trade-off between stability and accuracy: smaller values of f tend to improve numerical stability, yet deteriorate the accuracy of the partitioned solution. Using the simplified FSI model, the critical value of f that optimizes this trade-off is derived and discussed.KEYWORDS embedded boundary method, fluid-structure interaction, numerical added-mass effect, partitioned procedure, Robin-Neumann transmission conditions 578