180 research outputs found
Symmetrized Operator Split Schemes for Force and Source Modeling in Cascaded Lattice Boltzmann Methods for Flow and Scalar Transport
Operator split forcing schemes exploiting a symmetrization principle, i.e.
Strang splitting, for cascaded lattice Boltzmann (LB) methods in two- and
three-dimensions for fluid flows with impressed local forces are presented.
Analogous scheme for the passive scalar transport represented by a
convection-diffusion equation with a source term in a novel cascaded LB
formulation is also derived. They are based on symmetric applications of the
split solutions of the changes on the scalar field/fluid momentum due to the
sources/forces over half time steps before and after the collision step. The
latter step is effectively represented in terms of the post-collision change of
moments at zeroth and first orders, respectively, to represent the effect of
the sources on the scalar transport and forces on the fluid flow. Such
symmetrized operator split cascaded LB schemes are consistent with the
second-order Strang splitting and naturally avoid any discrete effects due to
forces/sources by appropriately projecting their effects for higher order
moments. All the force/source implementation steps are performed only in the
moment space and they do not require formulations as extra terms and their
additional transformations to the velocity space. These result in particularly
simpler and efficient schemes to incorporate forces/sources in the cascaded LB
methods unlike those considered previously. Numerical study for various
benchmark problems in 2D and 3D for fluid flow problems with body forces and
scalar transport with sources demonstrate the validity and accuracy, as well as
the second-order convergence rate of the symmetrized operator split
forcing/source schemes for the cascaded LB methods.Comment: 41 pages, 9 figure
Galilean Invariant Preconditioned Central Moment Lattice Boltzmann Method without Cubic Velocity Errors for Efficient Steady Flow Simulations
Lattice Boltzmann (LB) models used for the computation of fluid flows
represented by the Navier-Stokes (NS) equations on standard lattices can lead
to non-Galilean invariant (GI) viscous stress involving cubic velocity errors.
This arises from the dependence of their third order diagonal moments on the
first order moments for standard lattices, and strategies have recently been
introduced to restore GI without such errors using a modified collision
operator involving either corrections to the relaxation times or to the moment
equilibria. Convergence acceleration in the simulation of steady flows can be
achieved by solving the preconditioned NS equations, which contain a
preconditioning parameter that alleviates the numerical stiffness. In the
present study, we present a GI formulation of the preconditioned cascaded
central moment LB method used to solve the preconditioned NS equations, which
is free of cubic velocity errors on a standard lattice. A Chapman-Enskog
analysis reveals the structure of the spurious non-GI defect terms and it is
demonstrated that the anisotropy of the resulting viscous stress is dependent
on the preconditioning parameter, in addition to the fluid velocity. It is
shown that partial correction to eliminate the cubic velocity defects is
achieved by scaling the cubic velocity terms in the off-diagonal third-order
moment equilibria with the square of the preconditioning parameter.
Furthermore, we develop additional corrections based on the extended moment
equilibria involving gradient terms with coefficients dependent locally on the
fluid velocity and the preconditioning parameter. Several conclusions are drawn
from the analysis of the structure of the non-GI errors and the associated
corrections, with particular emphasis on their dependence on the
preconditioning parameter. Improvements in accuracy and convergence
acceleration are demonstrated.Comment: 43 pages, 14 figure
Central Moments-based Cascaded Lattice Boltzmann Method for Thermal Convective Flows in Three-Dimensions
Fluid motion driven by thermal effects, such as that due to buoyancy in
differentially heated three-dimensional (3D) enclosures, arise in several
natural settings and engineering applications. It is represented by the
solutions of the Navier-Stokes equations (NSE) in conjunction with the thermal
energy transport equation represented as a convection-diffusion equation (CDE)
for the temperature field. In this study, we develop new 3D lattice Boltzmann
(LB) methods based on central moments and using multiple relaxation times for
the three-dimensional, fifteen velocity (D3Q15) lattice, as well as it subset,
i.e. the three-dimensional, seven velocity (D3Q7) lattice to solve the 3D CDE
for the temperature field in a double distribution function framework. Their
collision operators lead to a cascaded structure involving higher order terms
resulting in improved stability. In this approach, the fluid motion is solved
by another 3D cascaded LB model from prior work. Owing to the differences in
the number of collision invariants to represent the dynamics of flow and the
transport of the temperature field, the structure of the collision operator for
the 3D cascaded LB formulation for the CDE is found to be markedly different
from that for the NSE. The new 3D cascaded (LB) models for thermal convective
flows are validated for natural convection of air driven thermally on two
vertically opposite faces in a cubic cavity enclosure at different Rayleigh
numbers against prior numerical benchmark solutions. Results show good
quantitative agreement of the profiles of the flow and thermal fields, and the
magnitudes of the peak convection velocities as well as the heat transfer rates
given in terms of the Nusselt number.Comment: 38 pages, 4 figures; typos corrected & figures 3 and 4 modifie
Cascaded Lattice Boltzmann Method based on Central Moments for Axisymmetric Thermal Flows Including Swirling Effects
A cascaded lattice Boltzmann (LB) approach based on central moments and
multiple relaxation times to simulate thermal convective flows, which are
driven by buoyancy forces and/or swirling effects, in the cylindrical
coordinate system with axial symmetry is presented. In this regard, the
dynamics of the axial and radial momentum components along with the pressure
are represented by means of the 2D Navier-Stokes equations with geometric mass
and momentum source terms in the pseudo Cartesian form, while the evolutions of
the azimuthal momentum and the temperature field are each modeled by an
advection-diffusion type equation with appropriate local source terms. Based on
these, cascaded LB schemes involving three distribution functions are
formulated to solve for the fluid motion in the meridian plane using a D2Q9
lattice, and to solve for the azimuthal momentum and the temperature field each
using a D2Q5 lattice. The geometric mass and momentum source terms for the flow
fields and the energy source term for the temperature field are included using
a new symmetric operator splitting technique, via pre-collision and
post-collision source steps around the cascaded collision step for each
distribution function. These result in a particularly simple and compact
formulation to directly represent the effect of various geometric source terms
consistently in terms of changes in the appropriate zeroth and first order
moments. Simulations of several complex buoyancy-driven thermal flows and
including rotational effects in cylindrical geometries using the new
axisymmetric cascaded LB schemes show good agreement with prior benchmark
results for the structures of the velocity and thermal fields as well as the
heat transfer rates given in terms of the Nusselt numbers.Comment: 49 pages,12 figure
Local Vorticity Computation in Double Distribution Functions based Lattice Boltzmann Methods for Flow and Scalar Transport
Computation of vorticity in conjunction with the strain rate tensor, plays an
important role in fluid mechanics in vortical structure identification and in
the modeling of various complex fluids. For the simulation of flows accompanied
by the advection-diffusion transport of a scalar field, double distribution
functions (DDF) based lattice Boltzmann methods (LBMs) are commonly used. We
present a new local vorticity computation approach by introducing an
intensional anisotropy of the scalar flux in the third order, off-diagonal
moment equilibria of the LB scheme for the scalar field, and then combining the
second order non-equilibrium components of both the LBMs. As such, any pair of
lattice sets in the DDF formulation that can independently support the third
order off-diagonal moments would enable local determination of the complete
flow kinematics, with the LBMs for the fluid motion and the transport of the
passive scalar respectively providing the necessary moment relationships to
determine the symmetric and skew-symmetric components of the velocity gradient
tensor. Since the resulting formulation is completely local and do not rely on
finite difference approximations for velocity derivatives, it is by design
naturally suitable for parallel computation. As an illustration of our
approach, we formulate a DDF-LB scheme for local vorticity computation using a
pair of multiple relaxation times (MRT) based collision approaches on
two-dimensional, nine velocity (D2Q9) lattices, where the necessary moment
relationships to determine the velocity gradient tensor and the vorticity are
established via a Chapman-Enskog analysis. Simulations of various benchmark
flows demonstrate good accuracy of the predicted vorticity fields, with a
second order convergence. Furthermore, extensions of our formulation for a
variety of collision models to enable local vorticity computation are
presented.Comment: 48 pages, 6 figures; A three-dimensional version of the local
vorticity computation approach in double distribution functions-based LB
models on standard lattices using different collision models was presented at
the 16th International Conference on Mesoscopic Methods in Engineering
Science (ICMMES 2019) in Edinburgh, UK which will be reported separatel
Adaptive Real-Time Removal of Impulse Noise in Medical Images
Noise is an important factor that degrades the quality of medical images.
Impulse noise is a common noise, which is caused by malfunctioning of sensor
elements or errors in the transmission of images. In medical images due to
presence of white foreground and black background, many pixels have intensities
similar to impulse noise and distinction between noisy and regular pixels is
difficult. In software techniques, the accuracy of the noise removal is more
important than the algorithm's complexity. But for hardware implementation
having a low complexity algorithm with an acceptable accuracy is essential. In
this paper a low complexity de-noising method is proposed that removes the
noise by local analysis of the image blocks. The proposed method distinguishes
non-noisy pixels that have noise-like intensities. All steps are designed to
have low hardware complexity. Simulation results show that for different
magnetic resonance images, the proposed method removes impulse noise with an
acceptable accuracy.Comment: 9 pages, 12 figures, 2 table
Cascaded Lattice Boltzmann Modeling and Simulations of Three-Dimensional Non-Newtonian Fluid Flows
Non-Newtonian fluid flows, especially in three dimensions (3D), arise in
numerous settings of interest to physics. Prior studies using the lattice
Boltzmann method (LBM) of such flows have so far been limited to mainly to two
dimensions and used less robust collision models. In this paper, we develop a
new 3D cascaded LBM based on central moments and multiple relaxation times on a
three-dimensional, nineteen velocity (D3Q19) lattice for simulation of
generalized Newtonian (power law) fluid flows. The relaxation times of the
second order moments are varied locally based on the local shear rate and
parameterized by the consistency coefficient and the power law index of the
nonlinear constitutive relation of the power law fluid. Numerical validation
study of the 3D cascaded LBM for various benchmark problems, including the
complex 3D non-Newtonian flow in a cubic cavity at different Reynolds numbers
and power law index magnitudes encompassing shear thinning and shear thickening
fluids, are presented. Furthermore, numerical stability comparisons of the
proposed advanced LBM scheme against the LBM based on other collision models,
such as the SRT model and MRT model based on raw moments, are made. Numerical
results demonstrate the accuracy, second order grid convergence and significant
improvements in stability of the 3D cascaded LBM for simulation of 3D
non-Newtonian flows of power law fluids.Comment: 41 pages, 14 figures, To appear in Computer Physics Communication
Multiple Abnormality Detection for Automatic Medical Image Diagnosis Using Bifurcated Convolutional Neural Network
Automating classification and segmentation process of abnormal regions in
different body organs has a crucial role in most of medical imaging
applications such as funduscopy, endoscopy, and dermoscopy. Detecting multiple
abnormalities in each type of images is necessary for better and more accurate
diagnosis procedure and medical decisions. In recent years portable medical
imaging devices such as capsule endoscopy and digital dermatoscope have been
introduced and made the diagnosis procedure easier and more efficient. However,
these portable devices have constrained power resources and limited
computational capability. To address this problem, we propose a bifurcated
structure for convolutional neural networks performing both classification and
segmentation of multiple abnormalities simultaneously. The proposed network is
first trained by each abnormality separately. Then the network is trained using
all abnormalities. In order to reduce the computational complexity, the network
is redesigned to share some features which are common among all abnormalities.
Later, these shared features are used in different settings (directions) to
segment and classify the abnormal region of the image. Finally, results of the
classification and segmentation directions are fused to obtain the classified
segmentation map. Proposed framework is simulated using four frequent
gastrointestinal abnormalities as well as three dermoscopic lesions and for
evaluation of the proposed framework the results are compared with the
corresponding ground truth map. Properties of the bifurcated network like low
complexity and resource sharing make it suitable to be implemented as a part of
portable medical imaging devices
Modeling Neural Architecture Search Methods for Deep Networks
There are many research works on the designing of architectures for the deep
neural networks (DNN), which are named neural architecture search (NAS)
methods. Although there are many automatic and manual techniques for NAS
problems, there is no unifying model in which these NAS methods can be explored
and compared. In this paper, we propose a general abstraction model for NAS
methods. By using the proposed framework, it is possible to compare different
design approaches for categorizing and identifying critical areas of interest
in designing DNN architectures. Also, under this framework, different methods
in the NAS area are summarized; hence a better view of their advantages and
disadvantages is possible.Comment: 6 pages, 7 figure
Modeling of Pruning Techniques for Deep Neural Networks Simplification
Convolutional Neural Networks (CNNs) suffer from different issues, such as
computational complexity and the number of parameters. In recent years pruning
techniques are employed to reduce the number of operations and model size in
CNNs. Different pruning methods are proposed, which are based on pruning the
connections, channels, and filters. Various techniques and tricks accompany
pruning methods, and there is not a unifying framework to model all the pruning
methods. In this paper pruning methods are investigated, and a general model
which is contained the majority of pruning techniques is proposed. The
advantages and disadvantages of the pruning methods can be identified, and all
of them can be summarized under this model. The final goal of this model is to
provide a general approach for all of the pruning methods with different
structures and applications.Comment: six pages, eight figure
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