33,407 research outputs found
Lattice Boltzmann model approximated with finite difference expressions
We show that the asymptotic properties of the link-wise artificial
compressibility method are not compatible with a correct approximation of fluid
properties. We propose to adapt the previous method through a framework
suggested by the Taylor expansion method and to replace first order terms in
the expansion by appropriate three or five points finite differences and to add
non linear terms. The "FD-LBM" scheme obtained by this method is tested in two
dimensions for shear wave, Stokes modes and Poiseuille flow. The results are
compared with the usual lattice Boltzmann method in the framework of multiple
relaxation times
Curious convergence properties of lattice Boltzmann schemes for diffusion with acoustic scaling
We consider the D1Q3 lattice Boltzmann scheme with an acoustic scale for the
simulation of diffusive processes. When the mesh is refined while holding the
diffusivity constant, we first obtain asymptotic convergence. When the mesh
size tends to zero, however, this convergence breaks down in a curious fashion,
and we observe qualitative discrepancies from analytical solutions of the heat
equation. In this work, a new asymptotic analysis is derived to explain this
phenomenon using the Taylor expansion method, and a partial differential
equation of acoustic type is obtained in the asymptotic limit. We show that the
error between the D1Q3 numerical solution and a finite-difference approximation
of this acoustic-type partial differential equation tends to zero in the
asymptotic limit. In addition, a wave vector analysis of this asymptotic regime
demonstrates that the dispersion equation has nontrivial complex eigenvalues, a
sign of underlying propagation phenomena, and a portent of the unusual
convergence properties mentioned above
Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics
The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool
for aeroacoustic computations. However, the LBM has been shown to present
accuracy and stability issues in the medium-low Mach number range, that is of
interest for aeroacoustic applications. Several solutions have been proposed
but often are too computationally expensive, do not retain the simplicity and
the advantages typical of the LBM, or are not described well enough to be
usable by the community due to proprietary software policies. We propose to use
an original regularized collision operator, based on the expansion in Hermite
polynomials, that greatly improves the accuracy and stability of the LBM
without altering significantly its algorithm. The regularized LBM can be easily
coupled with both non-reflective boundary conditions and a multi-level grid
strategy, essential ingredients for aeroacoustic simulations. Excellent
agreement was found between our approach and both experimental and numerical
data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder
and the 3D turbulent jet. Finally, most of the aeroacoustic computations with
LBM have been done with commercial softwares, while here the entire theoretical
framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of
America (in press
Real-time lattice boltzmann shallow waters method for breaking wave simulations
We present a new approach for the simulation of surfacebased fluids based in a hybrid formulation of Lattice Boltzmann Method for Shallow Waters and particle systems. The modified LBM can handle arbitrary underlying terrain conditions and arbitrary fluid depth. It also introduces a novel method for tracking dry-wet regions and moving boundaries. Dynamic rigid bodies are also included in our simulations using a two-way coupling. Certain features of the simulation that the LBM can not handle because of its heightfield nature, as breaking waves, are detected and automatically turned into splash particles. Here we use a ballistic particle system, but our hybrid method can handle more complex systems as SPH. Both the LBM and particle systems are implemented in CUDA, although dynamic rigid bodies are simulated in CPU. We show the effectiveness of our method with various examples which achieve real-time on consumer-level hardware.Peer ReviewedPostprint (author's final draft
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