5,279 research outputs found
A full Eulerian finite difference approach for solving fluid-structure coupling problems
A new simulation method for solving fluid-structure coupling problems has
been developed. All the basic equations are numerically solved on a fixed
Cartesian grid using a finite difference scheme. A volume-of-fluid formulation
(Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely
used for multiphase flow simulations, is applied to describing the
multi-component geometry. The temporal change in the solid deformation is
described in the Eulerian frame by updating a left Cauchy-Green deformation
tensor, which is used to express constitutive equations for nonlinear
Mooney-Rivlin materials. In this paper, various verifications and validations
of the present full Eulerian method, which solves the fluid and solid motions
on a fixed grid, are demonstrated, and the numerical accuracy involved in the
fluid-structure coupling problems is examined.Comment: 38 pages, 27 figures, accepted for publication in J. Comput. Phy
Simulating water-entry/exit problems using Eulerian-Lagrangian and fully-Eulerian fictitious domain methods within the open-source IBAMR library
In this paper we employ two implementations of the fictitious domain (FD)
method to simulate water-entry and water-exit problems and demonstrate their
ability to simulate practical marine engineering problems. In FD methods, the
fluid momentum equation is extended within the solid domain using an additional
body force that constrains the structure velocity to be that of a rigid body.
Using this formulation, a single set of equations is solved over the entire
computational domain. The constraint force is calculated in two distinct ways:
one using an Eulerian-Lagrangian framework of the immersed boundary (IB) method
and another using a fully-Eulerian approach of the Brinkman penalization (BP)
method. Both FSI strategies use the same multiphase flow algorithm that solves
the discrete incompressible Navier-Stokes system in conservative form. A
consistent transport scheme is employed to advect mass and momentum in the
domain, which ensures numerical stability of high density ratio multiphase
flows involved in practical marine engineering applications. Example cases of a
free falling wedge (straight and inclined) and cylinder are simulated, and the
numerical results are compared against benchmark cases in literature.Comment: The current paper builds on arXiv:1901.07892 and re-explains some
parts of it for the reader's convenienc
Simulations of propelling and energy harvesting articulated bodies via vortex particle-mesh methods
The emergence and understanding of new design paradigms that exploit flow
induced mechanical instabilities for propulsion or energy harvesting demands
robust and accurate flow structure interaction numerical models. In this
context, we develop a novel two dimensional algorithm that combines a Vortex
Particle-Mesh (VPM) method and a Multi-Body System (MBS) solver for the
simulation of passive and actuated structures in fluids. The hydrodynamic
forces and torques are recovered through an innovative approach which crucially
complements and extends the projection and penalization approach of Coquerelle
et al. and Gazzola et al. The resulting method avoids time consuming
computation of the stresses at the wall to recover the force distribution on
the surface of complex deforming shapes. This feature distinguishes the
proposed approach from other VPM formulations. The methodology was verified
against a number of benchmark results ranging from the sedimentation of a 2D
cylinder to a passive three segmented structure in the wake of a cylinder. We
then showcase the capabilities of this method through the study of an energy
harvesting structure where the stocking process is modeled by the use of
damping elements
A Vortex Method for Bi-phasic Fluids Interacting with Rigid Bodies
We present an accurate Lagrangian method based on vortex particles,
level-sets, and immersed boundary methods, for animating the interplay between
two fluids and rigid solids. We show that a vortex method is a good choice for
simulating bi-phase flow, such as liquid and gas, with a good level of realism.
Vortex particles are localized at the interfaces between the two fluids and
within the regions of high turbulence. We gain local precision and efficiency
from the stable advection permitted by the vorticity formulation. Moreover, our
numerical method straightforwardly solves the two-way coupling problem between
the fluids and animated rigid solids. This new approach is validated through
numerical comparisons with reference experiments from the computational fluid
community. We also show that the visually appealing results obtained in the CG
community can be reproduced with increased efficiency and an easier
implementation
Soft, slender and active structures in fluids: embedding Cosserat rods in vortex methods
We present a hybrid Eulerian-Lagrangian method for the direct simulation of
three-dimensional, heterogeneous structures made of soft fibers and immersed in
incompressible viscous fluids. Fiber-based organization of matter is pervasive
in nature and engineering, from biological architectures made of cilia, hair,
muscles or bones to polymers, composite materials or soft robots. In nature,
many such structures are adapted to manipulate flows for feeding, locomotion or
energy harvesting, through mechanisms that are often not fully understood.
While simulations can support the analysis (and subsequent translational
engineering) of these systems, extreme fibers' aspect-ratios, large elastic
deformations and two-way coupling with three-dimensional flows, all render the
problem numerically challenging. To address this, we couple Cosserat rod
theory, which exploits fibers' slenderness to capture their dynamics in
one-dimensional, accurate fashion, with vortex methods via a penalty immersed
boundary technique. The favorable properties of the resultant hydroelastic
solver are demonstrated against a battery of benchmarks, and further showcased
in a range of multi-physics scenarios, involving magnetic actuation, viscous
streaming, biomechanics, multi-body interaction, and self-propulsion.Comment: 28 pages, 12 figure
A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting
An explicit moving boundary method for the numerical solution of
time-dependent hyperbolic conservation laws on grids produced by the
intersection of complex geometries with a regular Cartesian grid is presented.
As it employs directional operator splitting, implementation of the scheme is
rather straightforward. Extending the method for static walls from Klein et
al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme
calculates fluxes needed for a conservative update of the near-wall cut-cells
as linear combinations of standard fluxes from a one-dimensional extended
stencil. Here the standard fluxes are those obtained without regard to the
small sub-cell problem, and the linear combination weights involve detailed
information regarding the cut-cell geometry. This linear combination of
standard fluxes stabilizes the updates such that the time-step yielding
marginal stability for arbitrarily small cut-cells is of the same order as that
for regular cells. Moreover, it renders the approach compatible with a wide
range of existing numerical flux-approximation methods. The scheme is extended
here to time dependent rigid boundaries by reformulating the linear combination
weights of the stabilizing flux stencil to account for the time dependence of
cut-cell volume and interface area fractions. The two-dimensional tests
discussed include advection in a channel oriented at an oblique angle to the
Cartesian computational mesh, cylinders with circular and triangular
cross-section passing through a stationary shock wave, a piston moving through
an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil
profile.Comment: 30 pages, 27 figures, 3 table
A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes
In this paper we show and discuss the use of a versatile interaction
potential approach coupled with an immersed boundary method to simulate a
variety of flows involving deformable bodies. In particular, we focus on two
kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii)
flow in the left ventricle of the heart with either a mechanical or a natural
valve. Both examples have in common the two-way interaction of the flow with a
deformable interface or a membrane. The interaction potential approach (de
Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura,
Computational Biomechanics, 2016) with minor modifications can be used to
capture the deformation dynamics in both classes of problems. We show that the
approach can be used to replicate the deformation dynamics of liquid-liquid
interfaces through the use of ad-hoc elastic constants. The results from our
simulations agree very well with previous studies on the deformation of drops
in standard flow configurations such as deforming drop in a shear flow or a
cross flow. We show that the same potential approach can also be used to study
the flow in the left ventricle of the heart. The flow imposed into the
ventricle interacts dynamically with the mitral valve (mechanical or natural)
and the ventricle which are simulated using the same model. Results from these
simulations are compared with ad- hoc in-house experimental measurements.
Finally, a parallelisation scheme is presented, as parallelisation is
unavoidable when studying large scale problems involving several thousands of
simultaneously deforming bodies on hundreds of distributed memory computing
processors
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