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

Real-Time Impulse Noise Removal from MR Images for Radiosurgery Applications

In the recent years image processing techniques are used as a tool to improve detection and diagnostic capabilities in the medical applications. Medical applications have been so much affected by these techniques which some of them are embedded in medical instruments such as MRI, CT and other medical devices. Among these techniques, medical image enhancement algorithms play an essential role in removal of the noise which can be produced by medical instruments and during image transfer. It has been proved that impulse noise is a major type of noise, which is produced during medical operations, such as MRI, CT, and angiography, by their image capturing devices. An embeddable hardware module which is able to denoise medical images before and during surgical operations could be very helpful. In this paper an accurate algorithm is proposed for real-time removal of impulse noise in medical images. All image blocks are divided into three categories of edge, smooth, and disordered areas. A different reconstruction method is applied to each category of blocks for the purpose of noise removal. The proposed method is tested on MR images. Simulation results show acceptable denoising accuracy for various levels of noise. Also an FPAG implementation of our denoising algorithm shows acceptable hardware resource utilization. Hence, the algorithm is suitable for embedding in medical hardware instruments such as radiosurgery devices.Comment: 12 pages, 13 figures, 2 table

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