A novel 3D variational aeroelastic framework for flexible multibody dynamics: Application to bat-like flapping dynamics

We present a novel three-dimensional (3D) variational aeroelastic framework for flapping wing with a flexible multibody system subjected to an external incompressible turbulent flow. The proposed aeroelastic framework consists of a three-dimensional fluid solver with delayed detached eddy simulation (DDES) and a nonlinear monolithic elastic structural solver for the flexible multibody system with constraints. Radial basis function (RBF) is applied in this framework to transfer the aerodynamic forces and structural displacements across the discrete non-matching interface meshes while satisfying a global energy conservation. The fluid equations are discretized using a stabilized Petrov-Galerkin method in space and the generalized-$\alpha$ approach is employed to integrate the solution in time. The flexible multibody system is solved by using geometrically exact co-rotational finite element method and an energy decaying scheme is used to achieve numerical stability of the multibody solver with constraints. A nonlinear iterative force correction (NIFC) scheme is applied in a staggered partitioned iterative manner to maintain the numerical stability of aeroelastic coupling with strong added mass effect. An isotropic aluminum wing with flapping motion is simulated via the proposed aeroelastic framework and the accuracy of the coupled solution is validated with the available experimental data. We next study the robustness and reliability of the 3D flexible multibody aeroelastic framework for an anisotropic flapping wing flight involving battens and membranes with composite material and compare against the experimental results. Finally, we demonstrate the aeroelastic framework for a bat-like wing and examine the effects of flexibility on the flapping wing dynamics.Comment: 53 page

An immersed boundary method for fluid--structure--acoustics interactions involving large deformations and complex geometries

This paper presents an immersed boundary (IB) method for fluid--structure--acoustics interactions involving large deformations and complex geometries. In this method, the fluid dynamics is solved by a finite difference method where the temporal, viscous and convective terms are respectively discretized by the third-order Runge-Kutta scheme, the fourth-order central difference scheme and a fifth-order W/TENO (Weighted/Targeted Essentially Non-oscillation) scheme. Without loss of generality, a nonlinear flexible plate is considered here, and is solved by a finite element method based on the absolute nodal coordinate formulation. The no-slip boundary condition at the fluid--structure interface is achieved by using a diffusion-interface penalty IB method. With the above proposed method, the aeroacoustics field generated by the moving boundaries and the associated flows are inherently solved. In order to validate and verify the current method, several benchmark cases are conducted: acoustic waves scattered from a stationary cylinder in a quiescent flow, sound generation by a stationary and a rotating cylinder in a uniform flow, sound generation by an insect in hovering flight, deformation of a red blood cell induced by acoustic waves and acoustic waves scattered by a stationary sphere. The comparison of the sound scattered by a cylinder shows that the present IB--WENO scheme, a simple approach, has an excellent performance which is even better than the implicit IB--lattice Boltzmann method. For the sound scattered by a sphere, the IB--TENO scheme has a lower dissipation compared with the IB--WENO scheme. Applications of this technique to model fluid-structure-acoustics interactions of flapping foils mimicking an insect wing section during forward flight and flapping foil energy harvester are also presented, considering the effects of foil shape and flexibility

Continuous-Scale Kinetic Fluid Simulation

Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches have not been widely adopted in graphics mainly due to the underlying inaccuracy, instability and inflexibility. In this paper, we try to tackle these problems in order to make kinetic approaches practical for graphical applications. To achieve more accurate and stable simulations, we propose to employ the non-orthogonal central-moment-relaxation model, where we develop a novel adaptive relaxation method to retain both stability and accuracy in turbulent flows. To achieve flexibility, we propose a novel continuous-scale formulation that enables samples at arbitrary resolutions to easily communicate with each other in a more continuous sense and with loose geometrical constraints, which allows efficient and adaptive sample construction to better match the physical scale. Such a capability directly leads to an automatic sample construction which generates static and dynamic scales at initialization and during simulation, respectively. This effectively makes our method suitable for simulating turbulent flows with arbitrary geometrical boundaries. Our simulation results with applications to smoke animations show the benefits of our method, with comparisons for justification and verification.Comment: 17 pages, 17 figures, accepted by IEEE Transactions on Visualization and Computer Graphic

Monolithic cut finite element based approaches for fluid-structure interaction

Cut finite element method (CutFEM) based approaches towards challenging fluid-structure interaction (FSI) are proposed. The different considered methods combine the advantages of competing novel Eulerian (fixed-grid) and established Arbitrary-Lagrangian-Eulerian (ALE) (moving mesh) finite element formulations for the fluid. The objective is to highlight the benefit of using cut finite element techniques for moving domain problems and to demonstrate their high potential with regards to simplified mesh generation, treatment of large structural motions in surrounding flows, capturing boundary layers, their ability to deal with topological changes in the fluid phase and their general straightforward extensibility to other coupled multiphysics problems. In addition to a pure fixed-grid FSI method, also advanced fluid domain decomposition techniques are considered rendering in highly flexible discretization methods for the FSI problem. All stabilized formulations include Nitsche-based weak coupling of the phases supported by the ghost penalty technique for the flow field. For the resulting systems, monolithic solution strategies are presented. Various 2D and 3D FSI-cases of different complexity validate the methods and demonstrate their capabilities and limitations in different situations.Comment: 41 pages, 16 figure

Fluid-structure interaction simulations of venous valves: a monolithic ALE method for large structural displacements

Venous valves are bicuspidal valves that ensure that blood in veins only flows back to the heart. To prevent retrograde blood flow, the two intraluminal leaflets meet in the center of the vein and occlude the vessel. In fluid-structure interaction (FSI) simulations of venous valves, the large structural displacements may lead to mesh deteriorations and entanglements, causing instabilities of the solver and, consequently, the numerical solution to diverge. In this paper, we propose an Arbitrary Lagrangian-Eulerian (ALE) scheme for FSI simulations designed to solve these instabilities. A monolithic formulation for the FSI problem is considered and, due to the complexity of the operators, the exact Jacobian matrix is evaluated using automatic differentiation. The method relies on the introduction of a staggered in time velocity %in the discretization scheme to improve stability, and on fictitious springs to model the contact force of the valve leaflets. Since the large structural displacements may compromise the quality of the fluid mesh as well, a smoother fluid displacement, obtained with the introduction of a scaling factor that measures the distance of a fluid element from the valve leaflet tip, guarantees that there are no mesh entanglements in the fluid domain. To further improve stability, a Streamline Upwind Petrov Galerkin (SUPG) method is employed. The proposed ALE scheme is applied to a 2D model of a venous valve. The presented simulations show that the proposed method deals well with the large structural displacements of the problem, allowing a reconstruction of the valve behavior in both the opening and closing phase

3D Common-Refinement Method for Non-Matching Meshes in Partitioned Variational Fluid-Structure Analysis

We present a three-dimensional (3D) common-refinement method for non-matching meshes between discrete non-overlapping subdomains of incompressible fluid and nonlinear hyperelastic structure. To begin, we first investigate the accuracy of common-refinement method (CRM) to satisfy traction equilibrium condition along the fluid-elastic interface with non-matching meshes. We systematically assess the accuracy of CRM against the matching grid solution by varying grid mismatch between the fluid and solid meshes over a cylindrical tubular elastic body. We demonstrate second-order accuracy of CRM through uniform refinements of fluid and solid meshes along the interface. We then extend the error analysis to transient data transfer across non-matching meshes between fluid and solid solvers. We show that the common-refinement discretization across non-matching fluid-structure grids yields accurate transfer of the physical quantities across the fluid-solid interface. We next solve a 3D benchmark problem of a cantilevered hyperelastic plate behind a circular bluff body and verify the accuracy of coupled solutions with respect to the available solution in the literature. By varying the solid interface resolution, we generate various non-matching grid ratios and quantify the accuracy of CRM for the nonlinear structure interacting with a laminar flow. We illustrate that the CRM with the partitioned NIFC treatment is stable for low solid-to-fluid density ratio and non-matching meshes. Finally, we demonstrate the 3D parallel implementation of common-refinement with NIFC scheme for a realistic engineering problem of drilling riser undergoing complex vortex-induced vibration with strong added mass effects.Comment: 38 pages, 16 figure

A parallel fluid solid coupling model using LAMMPS and Palabos based on the immersed boundary method

The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable solids exposed to flow. The code was validated with the Jeffery orbits of an ellipsoid particle in shear flow, red blood cell stretching test, and effective blood viscosity flowing in tubes. It demonstrated essentially linear scaling from 512 to 8192 cores for both strong and weak scaling cases. The computing time for the coupling increased with the solid fraction. An example of the fluid-solid coupling was given for flexible filaments (drug carriers) transport in a flowing blood cell suspensions, highlighting the advantages and capabilities of the developed code.Comment: For high resolution figure, see https://www.sciencedirect.com/science/article/pii/S187775031730981

Efficient Variable-Coefficient Finite-Volume Stokes Solvers

We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the success of using the classical projection method as a preconditioner for the coupled velocity-pressure system [B. E. Griffith, J. Comp. Phys., 228 (2009), pp. 75657595], as well as established techniques for steady and unsteady Stokes flow in the finite-element literature, we construct preconditioners that employ independent generalized Helmholtz and Poisson solvers for the velocity and pressure subproblems. We demonstrate that only a single cycle of a standard geometric multigrid algorithm serves as an effective inexact solver for each of these subproblems. Contrary to traditional wisdom, we find that the Stokes problem can be solved nearly as efficiently as the independent pressure and velocity subproblems, making the overall cost of solving the Stokes system comparable to the cost of classical projection or fractional step methods for incompressible flow, even for steady flow and in the presence of large density and viscosity contrasts. Two of the five preconditioners considered here are found to be robust to GMRES restarts and to increasing problem size, making them suitable for large-scale problems. Our work opens many possibilities for constructing novel unsplit temporal integrators for finite-volume spatial discretizations of the equations of low Mach and incompressible flow dynamics.Comment: Submitted to CiC

A stable partitioned FSI algorithm for incompressible flow and deforming beams

An added-mass partitioned (AMP) algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier-Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler-Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet-Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for one benchmark problem modeling blood flow in a deforming artery are also compared with corresponding results available in the literature

A variational flexible multibody formulation for partitioned fluid-structure interaction: Application to bat-inspired drones and unmanned air-vehicles

We present a three-dimensional (3D) partitioned aeroelastic formulation for a flexible multibody system interacting with incompressible turbulent fluid flow. While the incompressible Navier-Stokes system is discretized using a stabilized Petrov-Galerkin procedure, the multibody structural system consists of a generic interaction of multiple components such as rigid body, beams and flexible thin shells along with various types of joints and connections among them. A co-rotational framework is utilized for the category of small strain problems where the displacement of the body is decomposed into a rigid body rotation and a small strain component. This assumption simplifies the structural equations and allows for the incorporation of multiple bodies (rigid as well as flexible) in the system. The displacement and rotation constraints at the joints are imposed by a Lagrange multiplier method. The equilibrium conditions at the fluid-structure interface are satisfied by the transfer of tractions and structural displacements via the radial basis function approach, which is globally conservative. For the coupled stability in low structure-to-fluid mass ratio regimes, a nonlinear iterative force correction scheme is employed in the partitioned staggered predictor-corrector scheme. The convergence and generality of the radial basis function mapping are analyzed by carrying out systematic error analysis of the transfer of fluid traction across the non-matching fluid-structure interface where a third-order of convergence is observed. The proposed aeroelastic framework is then validated by considering a flow across a flexible pitching plate configuration with serration at the trailing edge. Finally, we demonstrate the flow across a flexible flapping wing of a bat modeling the bone fingers as beams and the flexible membrane as thin shells in the multibody system along with the joints.Comment: 34 pages, 20 figure