15,385 research outputs found
A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method
This paper deals with a new solid-fluid coupling algorithm between a rigid
body and an unsteady compressible fluid flow, using an Embedded Boundary
method. The coupling with a rigid body is a first step towards the coupling
with a Discrete Element method. The flow is computed using a Finite Volume
approach on a Cartesian grid. The expression of numerical fluxes does not
affect the general coupling algorithm and we use a one-step high-order scheme
proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The
Embedded Boundary method is used to integrate the presence of a solid boundary
in the fluid. The coupling algorithm is totally explicit and ensures exact mass
conservation and a balance of momentum and energy between the fluid and the
solid. It is shown that the scheme preserves uniform movement of both fluid and
solid and introduces no numerical boundary roughness. The effciency of the
method is demonstrated on challenging one- and two-dimensional benchmarks
A novel approach to rigid spheroid models in viscous flows using operator splitting methods
Calculating cost-effective solutions to particle dynamics in viscous flows is
an important problem in many areas of industry and nature. We implement a
second-order symmetric splitting method on the governing equations for a rigid
spheroidal particle model with torques, drag and gravity. The method splits the
operators into a vector field that is conservative and one that takes into
account the forces of the fluid. Error analysis and numerical tests are
performed on perturbed and stiff particle-fluid systems. For the perturbed
case, the splitting method greatly improves the solution accuracy, when
compared to a conventional multi-step method, and the global error behaves as
for roughly equal computational cost. For stiff
systems, we show that the splitting method retains stability in regimes where
conventional methods blow up. In addition, we show through numerical
experiments that the global order is reduced from
in the non-stiff regime to in
the stiff regime.Comment: 24 pages, 6 figures (13 if you count sub figs), all figures are in
colou
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 Discrete Theory of Connections on Principal Bundles
Connections on principal bundles play a fundamental role in expressing the
equations of motion for mechanical systems with symmetry in an intrinsic
fashion. A discrete theory of connections on principal bundles is constructed
by introducing the discrete analogue of the Atiyah sequence, with a connection
corresponding to the choice of a splitting of the short exact sequence.
Equivalent representations of a discrete connection are considered, and an
extension of the pair groupoid composition, that takes into account the
principal bundle structure, is introduced. Computational issues, such as the
order of approximation, are also addressed. Discrete connections provide an
intrinsic method for introducing coordinates on the reduced space for discrete
mechanics, and provide the necessary discrete geometry to introduce more
general discrete symmetry reduction. In addition, discrete analogues of the
Levi-Civita connection, and its curvature, are introduced by using the
machinery of discrete exterior calculus, and discrete connections.Comment: 38 pages, 11 figures. Fixed labels in figure
Passivity-preserving splitting methods for rigid body systems
A rigid body model for the dynamics of a marine vessel, used in simulations
of offshore pipe-lay operations, gives rise to a set of ordinary differential
equations with controls. The system is input-output passive. We propose
passivity-preserving splitting methods for the numerical solution of a class of
problems which includes this system as a special case. We prove the
passivity-preservation property for the splitting methods, and we investigate
stability and energy behaviour in numerical experiments. Implementation is
discussed in detail for a special case where the splitting gives rise to the
subsequent integration of two completely integrable flows. The equations for
the attitude are reformulated on using rotation matrices rather than
local parametrizations with Euler angles.Comment: 27 pages, 4 figures. To be published in 'Multibody System Dynamics
A fluctuating boundary integral method for Brownian suspensions
We present a fluctuating boundary integral method (FBIM) for overdamped
Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid
particles of complex shape immersed in a Stokes fluid. We develop a novel
approach for generating Brownian displacements that arise in response to the
thermal fluctuations in the fluid. Our approach relies on a first-kind boundary
integral formulation of a mobility problem in which a random surface velocity
is prescribed on the particle surface, with zero mean and covariance
proportional to the Green's function for Stokes flow (Stokeslet). This approach
yields an algorithm that scales linearly in the number of particles for both
deterministic and stochastic dynamics, handles particles of complex shape,
achieves high order of accuracy, and can be generalized to three dimensions and
other boundary conditions. We show that Brownian displacements generated by our
method obey the discrete fluctuation-dissipation balance relation (DFDB). Based
on a recently-developed Positively Split Ewald method [A. M. Fiore, F. Balboa
Usabiaga, A. Donev and J. W. Swan, J. Chem. Phys., 146, 124116, 2017],
near-field contributions to the Brownian displacements are efficiently
approximated by iterative methods in real space, while far-field contributions
are rapidly generated by fast Fourier-space methods based on fluctuating
hydrodynamics. FBIM provides the key ingredient for time integration of the
overdamped Langevin equations for Brownian suspensions of rigid particles. We
demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of
suspensions of starfish-shaped bodies using a random finite difference temporal
integrator.Comment: Submitted to J. Comp. Phy
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