Search results for: Boltzmann equation

Authors: Shashank Patidar, Sumit Kumar, Atul Srivastava, Suneet Singh

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Present work is concerned with the numerical investigation of thermal response of biological tissues during laser-based photo-thermal therapy for destroying cancerous/abnormal cells with minimal damage to the surrounding normal cells. Light propagation through the biological sample is mathematically modelled by transient radiative transfer equation. In the present work, application of the Lattice Boltzmann Method is extended to analyze transport of short-pulse radiation in a participating medium.In order to determine the two-dimensional temperature distribution inside the tissue medium, the RTE has been coupled with Penne’s bio-heat transfer equation based on Fourier’s law by several researchers in last few years.

Keywords: lattice Boltzmann method, transient radiation transfer equation, dual phase lag model

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Authors: Norjan Jumaa, David Graham

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We present a Lattice Boltzmann Method (LBM) for multiphase flows with high viscosity and density ratios. The motion of the interface between fluids is modelled by solving the Cahn-Hilliard (CH) equation with LBM. Incompressibility of the velocity fields in each phase is imposed by using a pressure correction scheme. We use a unified LBM approach with separate formulations for the phase field, the pressure less Naiver-Stokes (NS) equations and the pressure Poisson equation required for correction of the velocity field. The implementation has been verified for various test case. Here, we present results for some complex flow problems including two dimensional single and multiple mode Rayleigh-Taylor instability and we obtain good results when comparing with those in the literature. The main focus of our work is related to interactions between aerated or non-aerated waves and structures so we also present results for both high viscosity and low viscosity waves.

Keywords: lattice Boltzmann method, multiphase flows, Rayleigh-Taylor instability, waves

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Authors: Zaki Abiza, Miguel Chavez, David M. Holman, Ruddy Brionnaud

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In this paper, the prediction of the aerodynamic behavior of the flow around a Finned Projectile will be validated using a Computational Fluid Dynamics (CFD) solution, XFlow, based on the Lattice-Boltzmann Method (LBM). XFlow is an innovative CFD software developed by Next Limit Dynamics. It is based on a state-of-the-art Lattice-Boltzmann Method which uses a proprietary particle-based kinetic solver and a LES turbulent model coupled with the generalized law of the wall (WMLES). The Lattice-Boltzmann method discretizes the continuous Boltzmann equation, a transport equation for the particle probability distribution function. From the Boltzmann transport equation, and by means of the Chapman-Enskog expansion, the compressible Navier-Stokes equations can be recovered. However to simulate compressible flows, this method has a Mach number limitation because of the lattice discretization. Thanks to this flexible particle-based approach the traditional meshing process is avoided, the discretization stage is strongly accelerated reducing engineering costs, and computations on complex geometries are affordable in a straightforward way. The projectile that will be used in this work is the Army-Navy Basic Finned Missile (ANF) with a caliber of 0.03 m. The analysis will consist in varying the Mach number from M=0.5 comparing the axial force coefficient, normal force slope coefficient and the pitch moment slope coefficient of the Finned Projectile obtained by XFlow with the experimental data. The slope coefficients will be obtained using finite difference techniques in the linear range of the polar curve. The aim of such an analysis is to find out the limiting Mach number value starting from which the effects of high fluid compressibility (related to transonic flow regime) lead the XFlow simulations to differ from the experimental results. This will allow identifying the critical Mach number which limits the validity of the isothermal formulation of XFlow and beyond which a fully compressible solver implementing a coupled momentum-energy equations would be required.

Keywords: CFD, computational fluid dynamics, drag, finned projectile, lattice-boltzmann method, LBM, lift, mach, pitch

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Authors: Tobias Horstmann, Thomas Le Garrec, Daniel-Ciprian Mincu, Emmanuel Lévêque

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Despite the efficiency and low dissipation of the stream-collide formulation of the Lattice Boltzmann (LB) algorithm, which is nowadays implemented in many commercial LBM solvers, there are certain situations, e.g. mesh transition, in which a classical finite-volume or finite-difference formulation of the LB algorithm still bear advantages. In this paper, we present an algorithm that combines the node-based streaming of the distribution functions with a second-order finite volume discretization of the advection term of the BGK-LB equation on a uniform D2Q9 lattice. It is shown that such a coupling is possible for a multi-domain approach as long as the overlap, or buffer zone, between two domains, is achieved on at least 2Δx. This also implies that a direct coupling (without buffer zone) of a stream-collide and finite-volume LB algorithm on a single grid is not stable. The critical parameter in the coupling is the CFL number equal to 1 that is imposed by the stream-collide algorithm. Nevertheless, an explicit filtering step on the finite-volume domain can stabilize the solution. In a further investigation, we demonstrate how such a coupling can be used for mesh transition, resulting in an intrinsic conservation of mass over the interface.

Keywords: algorithm coupling, finite volume formulation, grid refinement, Lattice Boltzmann method

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Authors: Ishit Sheth, Chandrasekhar Jinendran, Chinmaya Ranjan Sahu

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A fourteen degree of freedom (DOF) ride and handling control mathematical model is developed for a car using generalized boltzmann hamel equation which will create a basis for design of ride and handling controller. Mathematical model developed yield equations of motion for non-holonomic constrained systems in quasi-coordinates. The governing differential equation developed integrates ride and handling control of car. Model-based systems engineering approach is implemented for simulation using matlab/simulink, vehicle’s response in different DOF is examined and later validated using commercial software (ADAMS). This manuscript involves detailed derivation of full car vehicle model which provides response in longitudinal, lateral and yaw motion to demonstrate the advantages of the developed model over the existing dynamic model. The dynamic behaviour of the developed ride and handling model is simulated for different road conditions.

Keywords: Full Vehicle Model, MBSE, Non Holonomic Constraints, Boltzmann Hamel Equation

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Authors: Ji-Hyok Kim, Il-Gyong Paek, Yong-Jun Kim

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We propose a numerical model based on drift-diffusion theory and lattice Boltzmann method (LBM) to analyze the electro-hydrodynamic behavior in low-pressure direct current (DC) glow discharge plasmas. We apply the drift-diffusion theory for 4-species and employ the standard lattice Boltzmann model (SLBM) for the electron, the finite difference-lattice Boltzmann model (FD-LBM) for heavy particles, and the finite difference model (FDM) for the electric potential, respectively. Our results are compared with those of other methods, and emphasize the necessity of a two-dimensional analysis for glow discharge.

Keywords: glow discharge, lattice Boltzmann method, numerical analysis, plasma simulation, electro-hydrodynamic

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Authors: Zainab D. Abd Ali, Thamir H. Khalaf

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In this paper, the characteristics of electric discharge in gap between two (parallel-plate) dielectric plates are studies, the gap filled with Argon gas in atm pressure at ambient temperature, the thickness of gap typically less than 1 mm and dielectric may be up 10 cm in diameter. One of dielectric plates a sinusoidal voltage is applied with Rf frequency, the other plates is electrically grounded. The simulation in this work depending on Boltzmann equation solver in first few moments, fluid model and plasma chemistry, in one dimensional modeling. This modeling have insight into characteristics of Dielectric Barrier Discharge through studying properties of breakdown of gas, electric field, electric potential, and calculating electron density, mean electron energy, electron current density ,ion current density, total plasma current density. The investigation also include: 1. The influence of change in thickness of gap between two plates if we doubled or reduced gap to half. 2. The effect of thickness of dielectric plates. 3. The influence of change in type and properties of dielectric material (gass, silicon, Teflon).

Keywords: computational diagnostics, Boltzmann equation, electric discharge, electron density

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Authors: H. Lee, Jr., L. Bo-ot, R. Tumlos, H. Ramos

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The objective of the study is to be able to calculate excitation and vibrational temperatures of a 2.45 GHz microwave-induced atmospheric pressure plasma jet. The plasma jet utilizes Argon gas as a primary working gas, while Nitrogen is utilized as a shroud gas for protecting the quartz tube from the plasma discharge. Through Optical Emission Spectroscopy (OES), various emission spectra were acquired from the plasma discharge. Selected lines from Ar I and N2 I emissions were used for the Boltzmann plot technique. The Boltzmann plots yielded values for the excitation and vibrational temperatures. The various values for the temperatures were plotted against varying parameters such as the gas flow rates.

Keywords: plasma jet, OES, Boltzmann plots, vibrational temperatures

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Authors: Lloyd G. Allred

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The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (E=mc²), then a relativistic correction is not required.

Keywords: cosmology, EMP, plasma physics, relativity

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Authors: K. S. Agrawal

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The performance of jet ejector was studied in detail by different authors. Several authors have studied mass transfer characteristics like interfacial area, mass transfer coefficients etc. In this paper, we have made an attempt to develop PDE model by considering bubble properties and apply Lattice-Boltzmann technique for PDE model. We may present the results for the interfacial area which we have obtained from our numerical simulation. Later the results are compared with previous work.

Keywords: jet ejector, mass transfer characteristics, numerical simulation, Lattice-Boltzmann technique

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Authors: Johan Loeckx, Joeri Bultheel

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Recently, the application of deep learning to music has gained popularity. Its true potential, however, has been largely unexplored. In this paper, a new idea for representing the dynamic behavior of music is proposed. A ”forward” conditional RBM takes into account not only preceding but also future samples during training. Though this may sound controversial at first sight, it will be shown that it makes sense from a musical and neuro-cognitive perspective. The model is applied to reconstruct music based upon the first notes and to improvise in the musical style of a composer. Different to expectations, reconstruction accuracy with respect to a regular CRBM with the same order, was not significantly improved. More research is needed to test the performance on unseen data.

Keywords: deep learning, restricted boltzmann machine, music generation, conditional restricted boltzmann machine (CRBM)

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Authors: Nastaran Ahmadpour Samani, Shahram Talebi

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Added mass is an important quantity in analysis of the motion of a submerged object ,which can be calculated by solving the equation of potential flow around the object . Here, we consider systems in which a square object is submerged in a channel of fluid and moves parallel to the wall. The corresponding added mass at a given distance from the wall d and for the object size s (which is the side of square object) is calculated via lattice Blotzmann simulation . By changing d and s separately, their effect on the added mass is studied systematically. The simulation results reveal that for the systems in which d > 4s, the distance does not influence the added mass any more. The added mass increases when the object approaches the wall and reaches its maximum value as it moves on the wall (d -- > 0). In this case, the added mass is about 73% larger than which of the case d=4s. In addition, it is observed that the added mass increases by increasing of the object size s and vice versa.

Keywords: Lattice Boltzmann simulation , added mass, square, variable size

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Authors: K. Noah, F.-S. Lien

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In Computational Fluid Dynamics (CFD), there are a variety of numerical methods, of which some depend on macroscopic model representatives. These models can be solved by finite-volume, finite-element or finite-difference methods on a microscopic description. However, the lattice Boltzmann method (LBM) is considered to be a mesoscopic particle method, with its scale lying between the macroscopic and microscopic scales. The LBM works well for solving incompressible flow problems, but certain limitations arise from solving compressible flows, particularly at high Mach numbers. An improved lattice Boltzmann model for compressible flow problems is presented in this research study. A higher-order Taylor series expansion of the Maxwell equilibrium distribution function is used to overcome limitations in LBM when solving high-Mach-number flows. Large eddy simulation (LES) is implemented in LBM to simulate turbulent jet flows. The results have been validated with available experimental data for turbulent compressible free jet flow at subsonic speeds.

Keywords: compressible lattice Boltzmann method, multiple relaxation times, large eddy simulation, turbulent jet flows

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Authors: Abir Yahya, Hacen Dhahri, Khalifa Slimi

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The present paper deals with a numerical simulation of temperature field inside a solid oxide fuel cell (SOFC) components. The temperature distribution is investigated using a co-flow planar SOFC comprising the air and fuel channel and two-ceramic electrodes, anode and cathode, separated by a dense ceramic electrolyte. The Lattice Boltzmann method (LBM) is used for the numerical simulation of the physical problem. The effects of inlet temperature, anode thermal conductivity and current density on temperature distribution are discussed. It was found that temperature distribution is very sensitive to the inlet temperature and the current density.

Keywords: heat sources, Lattice Boltzmann method, solid oxide fuel cell, temperature

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Authors: Jean Yves Trepanier, Sami Ammar, Sagnik Banik

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Lattice Boltzmann Method has been advantageous in simulating complex boundary conditions and solving for fluid flow parameters by streaming and collision processes. This paper includes the study of three different test cases in a confined domain using the method of the Lattice Boltzmann model. 1. An SRT (Single Relaxation Time) approach in the Lattice Boltzmann model is used to simulate Lid Driven Cavity flow for different Reynolds Number (100, 400 and 1000) with a domain aspect ratio of 1, i.e., square cavity. A moment-based boundary condition is used for more accurate results. 2. A Thermal Lattice BGK (Bhatnagar-Gross-Krook) Model is developed for the Rayleigh Benard convection for both test cases - Horizontal and Vertical Temperature difference, considered separately for a Boussinesq incompressible fluid. The Rayleigh number is varied for both the test cases (10^3 ≤ Ra ≤ 10^6) keeping the Prandtl number at 0.71. A stability criteria with a precise forcing scheme is used for a greater level of accuracy. 3. The phase change problem governed by the heat-conduction equation is studied using the enthalpy based Lattice Boltzmann Model with a single iteration for each time step, thus reducing the computational time. A double distribution function approach with D2Q9 (density) model and D2Q5 (temperature) model are used for two different test cases-the conduction dominated melting and the convection dominated melting. The solidification process is also simulated using the enthalpy based method with a single distribution function using the D2Q5 model to provide a better understanding of the heat transport phenomenon. The domain for the test cases has an aspect ratio of 2 with some exceptions for a square cavity. An approximate velocity scale is chosen to ensure that the simulations are within the incompressible regime. Different parameters like velocities, temperature, Nusselt number, etc. are calculated for a comparative study with the existing works of literature. The simulated results demonstrate excellent agreement with the existing benchmark solution within an error limit of ± 0.05 implicates the viability of this method for complex fluid flow problems.

Keywords: BGK, Nusselt, Prandtl, Rayleigh, SRT

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Authors: H. Hruschka

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This paper presents the first comparison of the performance of the restricted Boltzmann machine and the deep belief net on binary market basket data relative to binary factor analysis and the two best-known topic models, namely Dirichlet allocation and the correlated topic model. This comparison shows that the restricted Boltzmann machine and the deep belief net are superior to both binary factor analysis and topic models. Managerial implications that differ between the investigated models are treated as well. The restricted Boltzmann machine is defined as joint Boltzmann distribution of hidden variables and observed variables (purchases). It comprises one layer of observed variables and one layer of hidden variables. Note that variables of the same layer are not connected. The comparison also includes deep belief nets with three layers. The first layer is a restricted Boltzmann machine based on category purchases. Hidden variables of the first layer are used as input variables by the second-layer restricted Boltzmann machine which then generates second-layer hidden variables. Finally, in the third layer hidden variables are related to purchases. A public data set is analyzed which contains one month of real-world point-of-sale transactions in a typical local grocery outlet. It consists of 9,835 market baskets referring to 169 product categories. This data set is randomly split into two halves. One half is used for estimation, the other serves as holdout data. Each model is evaluated by the log likelihood for the holdout data. Performance of the topic models is disappointing as the holdout log likelihood of the correlated topic model – which is better than Dirichlet allocation - is lower by more than 25,000 compared to the best binary factor analysis model. On the other hand, binary factor analysis on its own is clearly surpassed by both the restricted Boltzmann machine and the deep belief net whose holdout log likelihoods are higher by more than 23,000. Overall, the deep belief net performs best. We also interpret hidden variables discovered by binary factor analysis, the restricted Boltzmann machine and the deep belief net. Hidden variables characterized by the product categories to which they are related differ strongly between these three models. To derive managerial implications we assess the effect of promoting each category on total basket size, i.e., the number of purchased product categories, due to each category's interdependence with all the other categories. The investigated models lead to very different implications as they disagree about which categories are associated with higher basket size increases due to a promotion. Of course, recommendations based on better performing models should be preferred. The impressive performance advantages of the restricted Boltzmann machine and the deep belief net suggest continuing research by appropriate extensions. To include predictors, especially marketing variables such as price, seems to be an obvious next step. It might also be feasible to take a more detailed perspective by considering purchases of brands instead of purchases of product categories.

Keywords: binary factor analysis, deep belief net, market basket analysis, restricted Boltzmann machine, topic models

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Authors: W. Hasan, H. Farhat, A. Alhilo, L. Tamimi

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Oil in water (O/W) emulsions are utilized extensively for cooling and lubricating cutting tools during parts machining. A robust Lattice Boltzmann (LBM) thermal-surfactants model, which provides a useful platform for exploring complex emulsions’ characteristics under variety of flow conditions, is used here for the study of the fluid behavior during conventional tools cooling. The transient thermal capabilities of the model are employed for simulating the effects of the flow conditions of O/W emulsions on the cooling of cutting tools. The model results show that the temperature outcome is slightly affected by reversing the direction of upper plate (workpiece). On the other hand, an important increase in effective viscosity is seen which supports better lubrication during the work.

Keywords: hybrid lattice Boltzmann method, Gunstensen model, thermal, surfactant-covered droplet, Marangoni stress

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Authors: W. Hasan, H. Farhat

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A hybrid quasi-steady thermal lattice Boltzmann model was used to study the combined effects of temperature and contact angle on the movement of slugs and droplets of oil in water (O/W) system flowing between two parallel plates. The model static contact angle due to the deposition of the O/W droplet on a flat surface with simulated hydrophilic characteristic at different fluid temperatures, matched very well the proposed theoretical calculation. Furthermore, the model was used to simulate the dynamic behavior of droplets and slugs deposited on the domain’s upper and lower surfaces, while subjected to parabolic flow conditions. The model accurately simulated the contact angle hysteresis for the dynamic droplets cases. It was also shown that at elevated temperatures the required power to transport the mixture diminished remarkably.

Keywords: lattice Boltzmann method, Gunstensen model, thermal, contact angle, high viscosity ratio

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Authors: Luma Al-Tamimi, Hassan Farhat, Wessam Hasan

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A three-dimensional (3D) hybrid quasi-steady thermal lattice Boltzmann model is developed to couple the effects of surfactant, temperature, interfacial tension, and contact angle. This 3D model is an extended scheme of a previously introduced two-dimensional (2D) hybrid lattice Boltzmann model. The 3D model is used to study the combined multi-physics effects on emulsion systems flowing in rectangular microchannels with and without confinements, where the suspended phase is made of droplets, plugs, or a mixture of both. The simulation results show that emulsion systems with plugs as the suspended phase are more efficient than with droplets, whereas mixed systems that form large plugs through coalescence have even greater efficiency. The 3D contact angle model generates matching results to those of the 2D model, which were validated with experiments. Furthermore, the effects of various confinements on adhering single drop systems are investigated for delineating their influence on the power required for transporting the suspended phase through the channel. It is shown that the deeper the constriction is, the lower the system efficiency. Increasing the surfactant concentration or fluid temperature in a channel with confinement carries a substantial positive effect on oil droplet transportation.

Keywords: lattice Boltzmann method, thermal, contact angle, surfactants, high viscosity ratio, porous media

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Authors: Souici Abdelaziz, Tehami Mohamed, Rahal Nacer, Said Mohamed Bekkouche, Berthet Jean-Fabien

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In this paper, the influence of the concrete slab creep on the initial deformability of a bent composite beam is modelled. This deformability depends on the rate of creep. This means the rise in value of the longitudinal strain ε c(x,t), the displacement D eflec(x,t) and the strain energy E(t). The variation of these three parameters can easily affect negatively the good appearance and the serviceability of the structure. Therefore, an analytical approach is designed to control the status of the deformability of the beam at the instant t. This approach is based on the Boltzmann’s superposition principle and very particularly on the irreversible law of deformation. For this, two conditions of compatibility and two other static equilibrium equations are adopted. The two first conditions are set according to the rheological equation of Dischinger. After having done a mathematical arrangement, we have reached a system of two differential equations whose integration allows to find the mathematical expression of each generalized internal force in terms of the ability of the concrete slab to creep.

Keywords: composite section, concrete, creep, deformation, differential equation, time

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Authors: Muhammad Yousaf, Shoaib Usman

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Numerical studies were conducted using Lattice Boltzmann Method (LBM) to study the natural convection in a square cavity in the presence of roughness. An algorithm basedon a single relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice Boltzmann Method (LBM) was developed. Roughness was introduced on both the hot and cold walls in the form of sinusoidal roughness elements. The study was conducted for a Newtonian fluid of Prandtl number (Pr) 1.0. The range of Ra number was explored from 103 to 106 in a laminar region. Thermal and hydrodynamic behavior of fluid was analyzed using a differentially heated square cavity with roughness elements present on both the hot and cold wall. Neumann boundary conditions were introduced on horizontal walls with vertical walls as isothermal. The roughness elements were at the same boundary condition as corresponding walls. Computational algorithm was validated against previous benchmark studies performed with different numerical methods, and a good agreement was found to exist. Results indicate that the maximum reduction in the average heat transfer was16.66 percent at Ra number 105.

Keywords: Lattice Boltzmann method, natural convection, nusselt number, rayleigh number, roughness

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Authors: Carlos Teodoro, Oscar Bautista

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In this work, we analyze theoretically the mass transport in a time-periodic electroosmotic flow through a parallel flat plate microchannel under different periodic functions of the applied external electric field. The microchannel connects two reservoirs having different constant concentrations of an electro-neutral solute, and the zeta potential of the microchannel walls are assumed to be uniform. The governing equations that allow determining the mass transport in the microchannel are given by the Poisson-Boltzmann equation, the modified Navier-Stokes equations, where the Debye-Hückel approximation is considered (the zeta potential is less than 25 mV), and the species conservation. These equations are nondimensionalized and four dimensionless parameters appear which control the mass transport phenomenon. In this sense, these parameters are an angular Reynolds, the Schmidt and the Péclet numbers, and an electrokinetic parameter representing the ratio of the half-height of the microchannel to the Debye length. To solve the mathematical model, first, the electric potential is determined from the Poisson-Boltzmann equation, which allows determining the electric force for various periodic functions of the external electric field expressed as Fourier series. In particular, three different excitation wave forms of the external electric field are assumed, a) sawteeth, b) step, and c) a periodic irregular functions. The periodic electric forces are substituted in the modified Navier-Stokes equations, and the hydrodynamic field is derived for each case of the electric force. From the obtained velocity fields, the species conservation equation is solved and the concentration fields are found. Numerical calculations were done by considering several binary systems where two dilute species are transported in the presence of a carrier. It is observed that there are different angular frequencies of the imposed external electric signal where the total mass transport of each species is the same, independently of the molecular diffusion coefficient. These frequencies are called crossover frequencies and are obtained graphically at the intersection when the total mass transport is plotted against the imposed frequency. The crossover frequencies are different depending on the Schmidt number, the electrokinetic parameter, the angular Reynolds number, and on the type of signal of the external electric field. It is demonstrated that the mass transport through the microchannel is strongly dependent on the modulation frequency of the applied particular alternating electric field. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.

Keywords: electroosmotic flow, mass transport, oscillatory flow, species separation

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Authors: Riki Dutta, Sagardeep Talukdar, Gautam Kumar Saharia, Sudipta Nandy

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Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics.

Keywords: conserved quantities, fokas-lenells equation, landau-lifshitz equation, lax pair

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Authors: Jian-Jun Shu

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It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Qijiao He

Abstract:

MicroElectrical-Mechanical System (MEMS) is one of the most rapidly developing frontier research field both in theory study and applied technology. Micro-channel is a very important link component of MEMS. With the research and development of MEMS, the size of the micro-devices and the micro-channels becomes further smaller. Compared with the macroscale flow, the flow characteristics of gas in the micro-channel have changed, and the rarefaction effect appears obviously. However, for the rarefied gas and microscale flow, Navier-Stokes-Fourier (NSF) equations are no longer appropriate due to the breakup of the continuum hypothesis. A Nonlinear Coupled Constitutive Model (NCCM) has been derived from the Boltzmann equation to describe the characteristics of both continuum and rarefied gas flows. We apply the present scheme to simulate continuum and rarefied gas flows in a micro-channel structure. And for comparison, we apply other widely used methods which based on particle simulation or direct solution of distribution function, such as Direct simulation of Monte Carlo (DSMC), Unified Gas-Kinetic Scheme (UGKS) and Lattice Boltzmann Method (LBM), to simulate the flows. The results show that the present solution is in better agreement with the experimental data and the DSMC, UGKS and LBM results than the NSF results in rarefied cases but is in good agreement with the NSF results in continuum cases. And some characteristics of both continuum and rarefied gas flows are observed and analyzed.

Keywords: continuum and rarefied gas flows, discontinuous Galerkin method, generalized hydrodynamic equations, numerical simulation

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Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Sanjit Kumar Paul, A. A. Mamun, M. R. Amin

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The Linear propagation of the dust-acoustic wave in a dusty plasma consisting of Boltzmann distributed electrons and ions and mobile charge fluctuating positive dust grains has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation and its responsible for the formation of the dust-acoustic waves in such a dusty plasma. The basic features of such dust-acoustic waves have been identified. It has been proposed to design a new laboratory experiment which will be able to identify the basic features of the dust-acoustic waves predicted in this theoretical investigation.

Keywords: dust acoustic waves, dusty plasma, Boltzmann distributed electrons, charge fluctuation

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Authors: Ganesh Meshram, Gloria Biswal

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In this study, we present the numerical investigation of surface wettability on triangular micropillar surfaces by using a two-dimensional (2D) pseudo-potential multiphase lattice Boltzmann method with a D2Q9 model for various interaction parameters of the range varies from -1.40 to -2.50. Initially, simulation of the equilibrium state of a water droplet on a flat surface is considered for various interaction parameters to examine the accuracy of the present numerical model. We then imposed the microscale pillars on the bottom wall of the surface with different heights of the pillars to form the hydrophobic and superhydrophobic surfaces which enable the higher contact angle. The wettability of surfaces is simulated with water droplets of radius 100 lattice units in the domain of 800x800 lattice units. The present study shows that increasing the interaction parameter of the pillared hydrophobic surfaces dramatically reduces the contact area between water droplets and solid walls due to the momentum redirection phenomenon. Contact angles for different values of interaction strength have been validated qualitatively with the analytical results.

Keywords: contact angle, lattice boltzmann method, d2q9 model, pseudo-potential multiphase method, hydrophobic surfaces, wenzel state, cassie-baxter state, wettability

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Authors: Jianjia Wang, Tong Yu, Haoran Zhu, Kun Liu, Jinwei Hao

Abstract:

The underlying pattern in the modern city is agglomeration. To some degree, the distribution of urban spatial density can be used to describe the status of this assemblage. There are three intrinsic characteristics to measure urban spatial density, namely, Floor Area Ratio (FAR), Building Coverage Ratio (BCR), and Average Storeys (AS). But the underlying mechanism that contributes to these quantities is still vague in the statistical urban study. In this paper, we explore the corresponding extrinsic factors related to spatial density. These factors can further provide the potential influence on the intrinsic quantities. Here, we take Shanghai Inner Ring Area and Manhattan in New York as examples to analyse the potential impacts on urban spatial density with six selected extrinsic elements. Ebery single factor presents the correlation to the spatial distribution, but the overall global impact of all is still implicit. To handle this issue, we attempt to develop the Boltzmann statistical model to explicitly explain the mechanism behind that. We derive a corresponding novel quantity, called capacity, to measure the global effects of all other extrinsic factors to the three intrinsic characteristics. The distribution of capacity presents a similar pattern to real measurements. This reveals the nonlinear influence on the multi-factor relations to the urban spatial density in agglomeration.

Keywords: urban spatial density, Boltzmann statistics, multi-factor correlation, spatial distribution

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

Abstract:

A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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