Two dimensional Lattice Boltzmann simulation of fluid flow through an idealized micro-structure of disordered media

This technical report discusses the application of Lattice Boltzmann Method (LBM) in the fluid flow simulation through porous filter-wall of disordered media. The diesel particulate filter (DPF) is an example of disordered media. DPF is developed as a cutting edge technology to reduce harmful particulate matter in the engine exhaust. Porous filter-wall of DPF traps these soot particles in the after-treatment of the exhaust gas. To examine the phenomena inside the DPF, researchers are looking forward to use the Lattice Boltzmann Method as a promising alternative simulation tool. The lattice Boltzmann method is comparatively a newer numerical scheme and can be used to simulate fluid flow for single-component single-phase, single-component multi-phase. It is also an excellent method for modelling flow through disordered media. The current work focuses on a single-phase fluid flow simulation inside the porous micro-structure using LBM. Firstly, the theory concerning the development of LBM is discussed. LBM evolution is always related to Lattice gas Cellular Automata (LGCA), but it is also shown that this method is a special discretized form of the continuous Boltzmann equation. Since all the simulations are conducted in two-dimensions, the equations developed are in reference with D2Q9 (two-dimensional 9-velocity) model. The artificially created porous micro-structure is used in this study. The flow simulations are conducted by considering air and CO2 gas as fluids. The numerical model used in this study is explained with a flowchart and the coding steps. The numerical code is constructed in MATLAB. Different types of boundary conditions and their importance is discussed separately. Also the equations specific to boundary conditions are derived. The pressure and velocity contours over the porous domain are studied and recorded. The results are compared with the published work. The permeability values obtained in this study can be fitted to the relation proposed by Nabovati [8], and the results are in excellent agreement within porosity range of 0.4 to 0.8.

LATTICE BOLTZMANN METHOD AND CELLULAR AUTOMATA SIMULATION OF PARTICLE MOTION AND DEPOSITION IN 2-D CASE

This technical report discusses the application of the Lattice Boltzmann Method (LBM) and Cellular Automata (CA) simulation in fluid flow and particle deposition. The current work focuses on incompressible flow simulation passing cylinders, in which we incorporate the LBM D2Q9 and CA techniques to simulate the fluid flow and particle loading respectively. For the LBM part, the theories of boundary conditions are studied and verified using the Poiseuille flow test. For the CA part, several models regarding simulation of particles are explained. And a new Digital Differential Analyzer (DDA) algorithm is introduced to simulate particle motion in the Boolean model. The numerical results are compared with a previous probability velocity model by Masselot [Masselot 2000], which shows a satisfactory result.

Carnot Cycles: Traditional and Stefan Boltzmann, and the First Planck Argument

The Stefan Boltzmann equation is obtained using a non-traditional Carnot Engine. In addition, the original Planck argument for radiation density is given.

Conductance interaction identification by means of Boltzmann distribution and mutual information analysis in conductance-based neuron models

Conductance interaction identification by means of Boltzmann distribution and mutual information analysis in conductance-based neuron models.

Learning higher-level features with convolutional restricted Boltzmann machines for sentiment analysis

In recent years, learning word vector representations has attracted much interest in Natural Language Processing. Word representations or embeddings learned using unsupervised methods help addressing the problem of traditional bag-of-word approaches which fail to capture contextual semantics. In this paper we go beyond the vector representations at the word level and propose a novel framework that learns higher-level feature representations of n-grams, phrases and sentences using a deep neural network built from stacked Convolutional Restricted Boltzmann Machines (CRBMs). These representations have been shown to map syntactically and semantically related n-grams to closeby locations in the hidden feature space. We have experimented to additionally incorporate these higher-level features into supervised classifier training for two sentiment analysis tasks: subjectivity classification and sentiment classification. Our results have demonstrated the success of our proposed framework with 4% improvement in accuracy observed for subjectivity classification and improved the results achieved for sentiment classification over models trained without our higher level features.

Lattice Boltzmann method for flow and heat transfer in microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice boltzmann modeling of fluid flow to determine the permeability of a karst specimen

A limestone sample was scanned using computed tomography (CT) and the hydraulic conductivity of the 3D reconstructed sample was determined using Lattice- Boltzmann methods (LBM) at varying scales. Due to the shape and size of the original sample, it was challenging to obtain a consistent rectilinear test sample. Through visual inspection however, 91 mm and 76 mm samples were digitally cut from the original. The samples had porosities of 58% and 64% and produced hydraulic conductivity values of K= 13.5 m/s and K=34.5 m/s, respectively. Both of these samples were re-sampled to 1/8 and 1/64 of their original size to produce new virtual samples at lower resolutions of 0.542 mm/lu and 1.084 mm/lu, while still representing the same physical dimensions. The hydraulic conductivity tended to increase slightly as the resolution became coarser. In order to determine an REV, the 91 mm sample was also sub-sampled into blocks that were 1/8 and 1/64 the size of the original. The results were consistent with analytical expectations such as those produced by the Kozeny-Carman equation. A definitive REV size was not reached, however, indicating the need for a larger sample. The methods described here demonstrate the ability of LBM to test rock structures and sizes not normally attainable.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice Boltzmann Method for Flow and Heat Transfer in Microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Reconstrução e reconhecimento de imagens binárias utilizando o algoritmo Máquina de Boltzmann

The objective of this work is to use algorithms known as Boltzmann Machine to rebuild and classify patterns as images. This algorithm has a similar structure to that of an Artificial Neural Network but network nodes have stochastic and probabilistic decisions. This work presents the theoretical framework of the main Artificial Neural Networks, General Boltzmann Machine algorithm and a variation of this algorithm known as Restricted Boltzmann Machine. Computer simulations are performed comparing algorithms Artificial Neural Network Backpropagation with these algorithms Boltzmann General Machine and Machine Restricted Boltzmann. Through computer simulations are analyzed executions times of the different described algorithms and bit hit percentage of trained patterns that are later reconstructed. Finally, they used binary images with and without noise in training Restricted Boltzmann Machine algorithm, these images are reconstructed and classified according to the bit hit percentage in the reconstruction of the images. The Boltzmann machine algorithms were able to classify patterns trained and showed excellent results in the reconstruction of the standards code faster runtime and thus can be used in applications such as image recognition.

Fully Anisotropic Solution of the Three Dimensional Boltzmann Transport Equation

The development of accurate modeling techniques for nanoscale thermal transport is an active area of research. Modern day nanoscale devices have length scales of tens of nanometers and are prone to overheating, which reduces device performance and lifetime. Therefore, accurate temperature profiles are needed to predict the reliability of nanoscale devices. The majority of models that appear in the literature obtain temperature profiles through the solution of the Boltzmann transport equation (BTE). These models often make simplifying assumptions about the nature of the quantized energy carriers (phonons). Additionally, most previous work has focused on simulation of planar two dimensional structures. This thesis presents a method which captures the full anisotropy of the Brillouin zone within a three dimensional solution to the BTE. The anisotropy of the Brillouin zone is captured by solving the BTE for all vibrational modes allowed by the Born Von-Karman boundary conditions.