6,709 research outputs found
A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions
A new parallel, computationally efficient immersed boundary method for
solving three-dimensional, viscous, incompressible flows on unbounded domains
is presented. Immersed surfaces with prescribed motions are generated using the
interpolation and regularization operators obtained from the discrete delta
function approach of the original (Peskin's) immersed boundary method. Unlike
Peskin's method, boundary forces are regarded as Lagrange multipliers that are
used to satisfy the no-slip condition. The incompressible Navier-Stokes
equations are discretized on an unbounded staggered Cartesian grid and are
solved in a finite number of operations using lattice Green's function
techniques. These techniques are used to automatically enforce the natural
free-space boundary conditions and to implement a novel block-wise adaptive
grid that significantly reduces the run-time cost of solutions by limiting
operations to grid cells in the immediate vicinity and near-wake region of the
immersed surface. These techniques also enable the construction of practical
discrete viscous integrating factors that are used in combination with
specialized half-explicit Runge-Kutta schemes to accurately and efficiently
solve the differential algebraic equations describing the discrete momentum
equation, incompressibility constraint, and no-slip constraint. Linear systems
of equations resulting from the time integration scheme are efficiently solved
using an approximation-free nested projection technique. The algebraic
properties of the discrete operators are used to reduce projection steps to
simple discrete elliptic problems, e.g. discrete Poisson problems, that are
compatible with recent parallel fast multipole methods for difference
equations. Numerical experiments on low-aspect-ratio flat plates and spheres at
Reynolds numbers up to 3,700 are used to verify the accuracy and physical
fidelity of the formulation.Comment: 32 pages, 9 figures; preprint submitted to Journal of Computational
Physic
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
An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary
Common efficient schemes for the incompressible Navier-Stokes equations, such
as projection or fractional step methods, have limited temporal accuracy as a
result of matrix splitting errors, or introduce errors near the domain
boundaries (which destroy uniform convergence to the solution). In this paper
we recast the incompressible (constant density) Navier-Stokes equations (with
the velocity prescribed at the boundary) as an equivalent system, for the
primary variables velocity and pressure. We do this in the usual way away from
the boundaries, by replacing the incompressibility condition on the velocity by
a Poisson equation for the pressure. The key difference from the usual
approaches occurs at the boundaries, where we use boundary conditions that
unequivocally allow the pressure to be recovered from knowledge of the velocity
at any fixed time. This avoids the common difficulty of an, apparently,
over-determined Poisson problem. Since in this alternative formulation the
pressure can be accurately and efficiently recovered from the velocity, the
recast equations are ideal for numerical marching methods. The new system can
be discretized using a variety of methods, in principle to any desired order of
accuracy. In this work we illustrate the approach with a 2-D second order
finite difference scheme on a Cartesian grid, and devise an algorithm to solve
the equations on domains with curved (non-conforming) boundaries, including a
case with a non-trivial topology (a circular obstruction inside the domain).
This algorithm achieves second order accuracy (in L-infinity), for both the
velocity and the pressure. The scheme has a natural extension to 3-D.Comment: 50 pages, 14 figure
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
cuIBM -- A GPU-accelerated Immersed Boundary Method
A projection-based immersed boundary method is dominated by sparse linear
algebra routines. Using the open-source Cusp library, we observe a speedup
(with respect to a single CPU core) which reflects the constraints of a
bandwidth-dominated problem on the GPU. Nevertheless, GPUs offer the capacity
to solve large problems on commodity hardware. This work includes validation
and a convergence study of the GPU-accelerated IBM, and various optimizations.Comment: Extended paper post-conference, presented at the 23rd International
Conference on Parallel Computational Fluid Dynamics (http://www.parcfd.org),
ParCFD 2011, Barcelona (unpublished
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