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1. Verification and convergence study of a spectral-element numerical methodology for fluid-structure interaction

   https://doi.org/doi.org/10.1016/j.jcpx.2021.100084  

   Xu, YiQin; Peet, Yulia T (March 2021, Journal of computational physics)

   A high-order in space spectral-element methodology for the solution of a strongly coupled fluid-structure interaction (FSI) problem is developed. A methodology is based on a partitioned solution of incompressible fluid equations on body-fitted grids, and nonlinearly-elastic solid deformation equations coupled via a fixed-point iteration approach with Aitken relaxation. A comprehensive verification strategy of the developed methodology is presented, including h-, p-and temporal refinement studies. An expected order of convergence is demonstrated first separately for the corresponding fluid and solid solvers, followed by a self-convergence study on a coupled FSI problem (self-convergence refers to a convergence to a reference solution obtained with the same solver at higher resolution). To this end, a new three-dimensional fluid-structure interaction benchmark is proposed for a verification of the FSI codes, which consists of a fluid flow in a channel with one rigid and one flexible wall. It is shown that, due to a consistent problem formulation, including initial and boundary conditions, a high-order spatial convergence on a fully coupled FSI problem can be demonstrated. Finally, a developed framework is applied successfully to a Direct Numerical Simulation of a turbulent flow in a channel interacting with a compliant wall, where the fluid-structure interface is fully resolved. 

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2. A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

   Kong, F.; Cai, X.-C. (March 2017, Journal of computational physics)

   Nonlinear fluid–structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. 

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3. Reduced-Order Modeling and Experimental Studies of Two-Way Coupled Fluid-Structure Interaction in Flapping Wings

   https://doi.org/10.1115/DETC2019-98291  

   Schwab, Ryan K.; Reid, Heidi E.; Jankauski, Mark A. (August 2019, Volume 8: 31st Conference on Mechanical Vibration and Noise)

   Abstract Flapping, flexible wings deform under both aerodynamic and inertial loads. However, the fluid-structure interaction (FSI) governing flapping wing dynamics is not well understood. Conventional FSI models require excessive computational resources and are not conducive to parameter studies that consider variable wing kinematics or geometry. Here, we present a simple two-way coupled FSI model for a wing subjected to single-degree-of-freedom (SDOF) rotation. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. We construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum to study our model experimentally. Overall, agreement between theory and experiment is excellent. In-vacuum, the wing has a large 3ω response when flapping at approximately 1/3 its natural frequency. This response is attenuated substantially when flapping in-air as a result of aerodynamic damping. These results highlight the importance of two-way coupling between the fluid and structure, since one-way coupled approaches cannot describe such phenomena. Moving forward, our model enables advanced studies of biological flight and facilitates bio-inspired design of flapping wing technologies. 

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4. Lagrangian vs. Eulerian: An Analysis of Two Solution Methods for Free-Surface Flows and Fluid Solid Interaction Problems

   https://doi.org/10.3390/fluids6120460  

   Rakhsha, Milad; Kees, Christopher E.; Negrut, Dan (December 2021, Fluids)

   As a step towards addressing a scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for the solution of free-surface and Fluid–Solid Interaction (FSI) problems. The Eulerian approach uses the Finite Element Method (FEM) to spatially discretize the Navier–Stokes equations. The free surface is handled via the volume-of-fluid (VOF) and the level-set (LS) equations; an Immersed Boundary Method (IBM) in conjunction with the Nitsche’s technique were applied to resolve the fluid–solid coupling. For the Lagrangian approach, the smoothed particle hydrodynamics (SPH) method is the meshless discretization technique of choice; no additional equations are needed to handle free-surface or FSI coupling. We compared the two approaches for a flow around cylinder. The dam break test was used to gauge the performance for free-surface flows. Lastly, the two approaches were compared on two FSI problems—one with a floating rigid body dropped into the fluid and one with an elastic gate interacting with the flow. We conclude with a discussion of the robustness, ease of model setup, and versatility of the two approaches. The Eulerian and Lagrangian solvers used in this study are open-source and available in the public domain. 

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5. Wind Turbine and Turbomachinery Computational Analysis with the ALE and Space-Time Variational Multiscale Methods and Isogeometric Discretization

   https://doi.org/10.25073/jaec.202041.278  

   Bazilevs, Yuri; Takizawa, Kenji; Tezduyar, Tayfun E.; Hsu, Ming-Chen; Otoguro, Yuto; Mochizuki, Hiroki; Wu, Michael C.H. (March 2020, Journal of Advanced Engineering and Computation)

   The challenges encountered in computational analysis of wind turbines and turbomachinery include turbulent rotational flows, complex geometries, moving boundaries and interfaces, such as the rotor motion, and the fluid-structure interaction (FSI), such as the FSI between the wind turbine blade and the air. The Arbitrary Lagrangian-Eulerian (ALE) and Space-Time (ST) Variational Multiscale (VMS) methods and isogeometric discretization have been effective in addressing these challenges. The ALE-VMS and ST-VMS serve as core computational methods. They are supplemented with special methods like the Slip Interface (SI) method and ST Isogeometric Analysis with NURBS basis functions in time. We describe the core and special methods and present, as examples of challenging computations performed, computational analysis of horizontaland vertical-axis wind turbines and flow-driven This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.string dynamics in pumps. 

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