1,851 research outputs found
An Immersed Boundary method with divergence-free velocity interpolation and force spreading
The Immersed Boundary (IB) method is a mathematical framework for
constructing robust numerical methods to study fluid-structure interaction in
problems involving an elastic structure immersed in a viscous fluid. The IB
formulation uses an Eulerian representation of the fluid and a Lagrangian
representation of the structure. The Lagrangian and Eulerian frames are coupled
by integral transforms with delta function kernels. The discretized IB
equations use approximations to these transforms with regularized delta
function kernels to interpolate the fluid velocity to the structure, and to
spread structural forces to the fluid. It is well-known that the conventional
IB method can suffer from poor volume conservation since the interpolated
Lagrangian velocity field is not generally divergence-free, and so this can
cause spurious volume changes. In practice, the lack of volume conservation is
especially pronounced for cases where there are large pressure differences
across thin structural boundaries. The aim of this paper is to greatly reduce
the volume error of the IB method by introducing velocity-interpolation and
force-spreading schemes with the properties that the interpolated velocity
field in which the structure moves is at least C1 and satisfies a continuous
divergence-free condition, and that the force-spreading operator is the adjoint
of the velocity-interpolation operator. We confirm through numerical
experiments in two and three spatial dimensions that this new IB method is able
to achieve substantial improvement in volume conservation compared to other
existing IB methods, at the expense of a modest increase in the computational
cost. Further, the new method provides smoother Lagrangian forces (tractions)
than traditional IB methods. The method presented here is restricted to
periodic computational domains. Its generalization to non-periodic domains is
important future work.Comment: 49 pages, 13 figure
An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver
We propose an efficient algorithm for the immersed boundary method on
distributed-memory architectures, with the computational complexity of a
completely explicit method and excellent parallel scaling. The algorithm
utilizes the pseudo-compressibility method recently proposed by Guermond and
Minev [Comptes Rendus Mathematique, 348:581-585, 2010] that uses a directional
splitting strategy to discretize the incompressible Navier-Stokes equations,
thereby reducing the linear systems to a series of one-dimensional tridiagonal
systems. We perform numerical simulations of several fluid-structure
interaction problems in two and three dimensions and study the accuracy and
convergence rates of the proposed algorithm. For these problems, we compare the
proposed algorithm against other second-order projection-based fluid solvers.
Lastly, the strong and weak scaling properties of the proposed algorithm are
investigated
Inertial Coupling Method for particles in an incompressible fluctuating fluid
We develop an inertial coupling method for modeling the dynamics of
point-like 'blob' particles immersed in an incompressible fluid, generalizing
previous work for compressible fluids. The coupling consistently includes
excess (positive or negative) inertia of the particles relative to the
displaced fluid, and accounts for thermal fluctuations in the fluid momentum
equation. The coupling between the fluid and the blob is based on a no-slip
constraint equating the particle velocity with the local average of the fluid
velocity, and conserves momentum and energy. We demonstrate that the
formulation obeys a fluctuation-dissipation balance, owing to the
non-dissipative nature of the no-slip coupling. We develop a spatio-temporal
discretization that preserves, as best as possible, these properties of the
continuum formulation. In the spatial discretization, the local averaging and
spreading operations are accomplished using compact kernels commonly used in
immersed boundary methods. We find that the special properties of these kernels
make the discrete blob a particle with surprisingly physically-consistent
volume, mass, and hydrodynamic properties. We develop a second-order
semi-implicit temporal integrator that maintains discrete
fluctuation-dissipation balance, and is not limited in stability by viscosity.
Furthermore, the temporal scheme requires only constant-coefficient Poisson and
Helmholtz linear solvers, enabling a very efficient and simple FFT-based
implementation on GPUs. We numerically investigate the performance of the
method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and
associated discussion) relative to published versio
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
Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations
The Immersed Boundary method has evolved into one of the most useful
computational methods in studying fluid structure interaction. On the other
hand, the Immersed Boundary method is also known to suffer from a severe
timestep stability restriction when using an explicit time discretization. In
this paper, we propose several efficient semi-implicit schemes to remove this
stiffness from the Immersed Boundary method for the two-dimensional Stokes
flow. First, we obtain a novel unconditionally stable semi-implicit
discretization for the immersed boundary problem. Using this unconditionally
stable discretization as a building block, we derive several efficient
semi-implicit schemes for the immersed boundary problem by applying the Small
Scale Decomposition to this unconditionally stable discretization. Our
stability analysis and extensive numerical experiments show that our
semi-implicit schemes offer much better stability property than the explicit
scheme. Unlike other implicit or semi-implicit schemes proposed in the
literature, our semi-implicit schemes can be solved explicitly in the spectral
space. Thus the computational cost of our semi-implicit schemes is comparable
to that of an explicit scheme, but with a much better stability property.Comment: 40 pages with 8 figure
A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies
We present a moving control volume (CV) approach to computing hydrodynamic
forces and torques on complex geometries. The method requires surface and
volumetric integrals over a simple and regular Cartesian box that moves with an
arbitrary velocity to enclose the body at all times. The moving box is aligned
with Cartesian grid faces, which makes the integral evaluation straightforward
in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of
velocity and pressure at the fluid-structure interface are avoided and
far-field (smooth) velocity and pressure information is used. We re-visit the
approach to compute hydrodynamic forces and torques through force/torque
balance equation in a Lagrangian frame that some of us took in a prior work
(Bhalla et al., J Comp Phys, 2013). We prove the equivalence of the two
approaches for IB methods, thanks to the use of Peskin's delta functions. Both
approaches are able to suppress spurious force oscillations and are in
excellent agreement, as expected theoretically. Test cases ranging from Stokes
to high Reynolds number regimes are considered. We discuss regridding issues
for the moving CV method in an adaptive mesh refinement (AMR) context. The
proposed moving CV method is not limited to a specific IB method and can also
be used, for example, with embedded boundary methods
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