Complicated Boundary Research Articles

About peculiarities of application of the method of fast expansions in the solution of the Navier-Stokes equations

The brief presentation of the method of fast expansions is given to solve nonlinear differential equations. Application rules of the operator of fast expansions are specified for solving differential equations. According to the method of fast expansions, an unknown function can be represented as the sum of the boundary function and Fourier series sines and cosines for one variable. The special construction of the boundary functions leads to reasonably fast convergence of the Fourier series, so that for engineering calculations, it is sufficient to consider only the first three members. The method is applicable both to linear and nonlinear integro-differential systems. By means of applying the method of fast expansions to nonlinear Navier-Stokes equations the problem is reduced to a closed system of ordinary differential equations, which solution doesn't represent special difficulties. We can reapply the method of fast expansions to the resulting system of differential equations and reduce the original problem to a system of algebraic equations. If the problem is n -dimensional, then after n -fold application of the method of fast expansions the problem will be reduced to a closed algebraic system. Finally, we obtain an analytic-form solution of complicated boundary value problem in partial derivatives. The flow of an incompressible viscous fluid of Navier–Stokes is considered in a curvilinear pipe. The problem is reduced to solving a closed system of ordinary differential equations with boundary conditions by the method of fast expansions. The article considers peculiarities of finding the coefficients of boundary functions and Fourier coefficients for the zero-order and first-order operators of fast expansions. Obtaining the analytic-form solution is of great interest, because it allows to analyze and to investigate the influence of various factors on the properties of the viscous fluid in specific cases.

Analysis of nano-bioconvection flow containing both nanoparticles and gyrotactic microorganisms in a horizontal channel using modified least square method (MLSM)

Abstract This paper purpose is to analyze the bioconvection nanofluid flow which contains both nanoparticles and gyrotactic microorganisms. We investigated a flow in a horizontal channel considering the model proposed by Kuznestov and Nield (2013). In this sort of problems, this model is more convenient and physical in comparison with other models. The least square method is utilized to solve the problem considering complicated boundary conditions. In addition, the impact of different parameters is investigated exhaustively on the temperature distribution profile, nanoparticle volume fraction and the density of motile microorganisms. It is found that such parameters can highly affect them particularly their stability. The effect of these parameters is much more obvious in vicinity of the channel walls.

Interactions between complicated flow-dispersion patterns and boundary layer evolution in a mountainous complex terrain during elevated SO2 concentrations

The dispersion of air pollutants from multiple industrial stacks located in complex topography is an interesting subject. An attractive case is that of the wider region of Western Macedonia in NW Greece, where the greater amount of electric power of Greece is being produced by lignite power plant stations (LPPS). Considerable amounts of atmospheric pollutants are emitted by those LPPS into the atmosphere due to the quantities of coal burned. The variability of the topographic features and the terrain complexity of the area may lead to the formation of local atmospheric circulations of various types, which affect pollutant’s transport and dispersion. In the present work, the dispersion conditions that favor the pollutants accumulation in the area are investigated. For this purpose, 1 year’s hourly SO2 concentrations, surface wind measurements and a mesoscale meteorological and air pollution model (The Air Pollution Model, TAPM) were used. The SO2 and wind measurements were collected in situ from monitoring stations located nearby and at a greater distance from the power plants. Yearly and daily variations of SO2 concentrations are analyzed and discussed, and the period with the highest concentrations is selected. During this period, the evolution of the atmospheric boundary layer (ABL) in the area as well as the pollutants dispersion is examined. Statistical measures between modeled and observed meteorological data were in good agreement and a good correlation coefficient 0.68 and 0.98 was found in the SO2 variations. The analysis of the wind fields indicated better ventilation in the center of the area due to topographic venturi effects, while the dispersion mechanism which resulted in the relatively high ground level concentrations was fumigation. Finally, the evolution of the ABL was affected by the complex interactions between topography and mesoscale flows as it was found by the turbulent kinetic energy cross sections.

A MACHINE LEARNS TO PREDICT THE STABILITY OF TIGHTLY PACKED PLANETARY SYSTEMS

ABSTRACT The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We show that characterizing the complicated and multi-dimensional stability boundary of tightly packed systems is amenable to machine-learning methods. We find that training an XGBoost machine-learning algorithm on physically motivated features yields an accurate classifier of stability in packed systems. On the stability timescale investigated (107 orbits), it is three orders of magnitude faster than direct N-body simulations. Optimized machine-learning classifiers for dynamical stability may thus prove useful across the discipline, e.g., to characterize the exoplanet sample discovered by the upcoming Transiting Exoplanet Survey Satellite. This proof of concept motivates investing computational resources to train algorithms capable of predicting stability over longer timescales and over broader regions of phase space.

Longitudinal vibration analysis of nonlocal nanorods with elastic end restraints by an improved Fourier series method

In this paper, an exact solution for the free longitudinal vibration of nanorod with arbitrary boundary conditions has been developed by an improved Fourier series method. Based on the nonlocal elasticity theory, the nanorod model with general boundary restraints has been formulated by introducing artificial springs and then all the classical boundary conditions can be simply realized by setting the spring stiffness to zero or infinity accordingly. With the aim to guarantee the differential continuities at both elastically restrained ends, the nonlocal axial displacement is invariantly expanded as the superposition of standard Fourier series and the auxiliary polynomials to ensure that the field function is sufficiently smooth in the whole region [0, L]. The problem is then tackled by solving the nonlocal governing equation and boundary conditions simultaneously in an exact manner. Numerical results are presented and compared with those in the literature to illustrate the reliability and effectiveness of the proposed model. The combined influences of small-scale parameter, boundary conditions and nanorod length on the longitudinal modal behavior are discussed and analyzed. This work can provide an efficient way for the longitudinal vibration characteristics study of nanorod, especially with complicated boundary conditions.

A DFFD simulation method combined with the spectral element method for solid–fluid-interaction problems

A 2D simulation method for a rigid body moving in an incompressible viscous fluid is proposed. It combines one of the immersed-boundary methods, the DFFD (direct forcing fictitious domain) method with the spectral element method; the former is employed for efficiently capturing the two-way FSI (fluid–structure interaction) and the geometric flexibility of the latter is utilized for any possibly co-existing stationary and complicated solid or flow boundary. A pseudo body force is imposed within the solid domain to enforce the rigid body motion and a Lagrangian mesh composed of triangular elements is employed for tracing the rigid body. In particular, a so called sub-cell scheme is proposed to smooth the discontinuity at the fluid–solid interface and to execute integrations involving Eulerian variables over the moving-solid domain. The accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literatures.

The finite dimensional global attractor for the 3D viscous Primitive Equations

A new method is presented to prove finiteness of the fractal and Hausdorff dimensions of the global attractor for the strong solutions to the 3D Primitive Equations (PEs) with viscosity, which is applicable to more general situations than the recent result of [8] in the sense that it removes all extra technical conditions imposed by previous analyses. More specifically, the dimensions of the global attractor are proved finite for heat source $Q\in L^2$, exactly the same condition for well-posedness of global strong solutions and existence of the global attractor of these solutions; while the best previous result obtained recently in [8] still requires the extra condition that $∂_zQ\in L^2$ for finiteness of the dimensions of the global attractor. The key new idea is that Ladyzhenskaya's squeezing property of the semigroup for the strong solutions can be established without higher solution regularity of Primitive Equations. This has the general interest for dissipative evolution equations. For this reason, the new method especially has the advantange of dealing with more complicated boundary conditions which present essential difficulties for previous methods. In particular, the case of 3D viscous PEs with `` physical boundary conditions'' can be treated by the new method in the same way as presented in this article, however, it seems rather difficult for previous methods.

Impact of interface misfit strain on the movement and tilt angles of the domain wall in ferroelectric thin films

The effect of interface misfit strain on the movement and tilt angles of the domain wall in ferroelectric thin film is investigated with a multicoupling finite element model. Since this theoretical model is developed based on the phase field method and is solved using the finite element method, it can effectively predict the electromechanical coupling behavior of materials that have complicated boundary conditions. The simulated results demonstrate that the position, tilt angles, strain gradient and energy density of the domain wall can be modulated by misfit compressive strain at the interface of ferroelectric nanostructures. A larger interface misfit compressive strain will lead to the movement of domain wall towards the direction which allows the [Formula: see text] domain to possess a larger volume. The difference of the tilt angles of domain walls on both sides of the [Formula: see text] domain becomes larger as the interface misfit strain increases, implying a transition of the shape of the [Formula: see text] domain from parallelogram to wedge.

Vibration Prediction Method of Electric Machines by using Experimental Transfer Function and Magnetostatic Finite Element Analysis

This paper concerns the noise and structural vibration caused by rotating electric machines. Special attention is given to the magnetic-force induced vibration response of interior-permanent magnet machines. In general, to accurately predict and control the vibration response caused by the electric machines, it is inevitable to model not only the magnetic force induced by the fluctuation of magnetic fields, but also the structural dynamic characteristics of the electric machines and surrounding structural components. However, due to complicated boundary conditions and material properties of the components, such as laminated magnetic cores and varnished windings, it has been a challenge to compute accurate vibration response caused by the electric machines even after their physical models are available. In this paper, we propose a highly-accurate vibration prediction method that couples experimentally-obtained discrete structural transfer functions and numerically-obtained distributed magnetic-forces. The proposed vibration synthesis methodology has been applied to predict vibration responses of an interior permanent magnet machine. The results show that the predicted vibration response of the electric machine agrees very well with the measured vibration response for several load conditions, for wide frequency ranges.

The Effect of Intergroup Cooperation in Video Games on Prejudice Reduction: Does This Effect Differ between Violent versus Nonviolent Games

Low frequency noise in duct is a challenge for the traditional passive noise control techniques. Recently, a so-called duct-membrane silencer has attracted much research attention due to its simple configuration and potential application, however, the current studies are merely limited to the cases in which just the classical boundary conditions are considered. Actually, as an important factor affecting the modal characteristics of the membrane, and the existing studies are not enough to fully understand the vibro-acoustic characteristics of such silencer with complicated boundary conditions. Motivated by this, in this paper, the structural–acoustic coupling model of duct-membrane system is established by a modified Fourier series method in combination with Rayleigh–Ritz procedure, in which the transverse elastic boundary restraints are taken into account. Energy principle is formulated for the vibro-acoustic coupling of such duct-membrane silencer to obtain the system matrix equation. Numerical results are then presented to validate the proposed model, and the influence of boundary restraining stiffness on sound attenuation performance is also studied. To the best of authors’ knowledge, this work represents the first time that the elastic boundary restraints have been considered for such duct-membrane silencing system.

Optimization of Lattice Boltzmann Simulation With Graphics-Processing-Unit Parallel Computing and the Application in Reservoir Characterization

Summary Shale permeability is sufficiently low to require an unconventional scale of stimulation treatments, such as very-large-volume, high-rate, multistage hydraulic-fracturing applications. Upscaling of hydrocarbon transport processes in shales is challenging because of the low permeability and strong heterogeneity. Rock characterization with high-resolution imaging [X-ray tomography and scanning electron microscope (SEM)] is usually highly localized and contains significant uncertainties because of the small field of view. Therefore, an effective high-performance computing method is required to collect information over a larger scale to meet the ergodicity requirement in upscaling. The lattice Boltzmann (LB) method has received significant attention in computational fluid dynamics because of its capability in coping with complicated boundary conditions. A combination of high-resolution imaging and LB simulation is a powerful approach for evaluating the transport properties of a porous medium in a timely manner, on the basis of the numerical solution of the Navier-Stokes equations and Darcy's law. In this work, a graphics-processing-unit (GPU) -enhanced lattice Boltzmann simulator (GELBS) was developed, which was optimized by GPU parallel computing on the basis of the inherent parallelism of the LB method. Specifically, the LB method was used to implement the computational kernel; a sparse data structure was applied to optimize memory allocation; the OCCA (Medina et al. 2014) portability library was used, which enables the GELBS codes to use different application-programming interfaces (APIs) including open computing language (OpenCL), compute unified device architecture (CUDA), and open multiprocessing (OpenMP). OpenCL is an open standard for cross-platform parallel computing, CUDA is supported only by NVIDIA devices, and OpenMP is primarily used on central processing units (CPUs). It was found that the GPU-accelerated code was approximately 1,000 times faster than the unoptimized serial code and 10 times faster than the parallel code run on a standalone CPU. The CUDA code was slightly faster than OpenCL code on the NVIDA GPU because of the extra cost of OpenCL used to adapt to a heterogeneous platform. The GELBS was validated by comparing it with analytical solutions, laboratory measurements, and other independent numerical simulators in previous studies, and it was proved to have a second-order global accuracy. The GELBS was then used to analyze thin cuttings extracted from a sandstone reservoir and a shale-gas reservoir. The sandstone permeabilities were found relatively isotropic, whereas the shale permeabilities were strongly anisotropic because of the horizontal lamination structure. In shale cuttings, the average permeability in the horizontal direction was higher than that in the vertical direction by approximately two orders of magnitude. Correlations between porosity and permeability were observed in both rocks. The combination of GELBS and high-resolution imaging methods makes for a powerful tool for permeability evaluation when conventional laboratory measurement is impossible because of small cuttings sizes. The constitutive correlations between geometry and transport properties can be used for upscaling in different rock types. The GPU-optimized code significantly accelerates the computing speed; thus, many more samples can be analyzed given the same processing time. Consequently, the ergodicity requirement is met, which leads to a better reservoir characterization.

Theoretical prediction of flange wrinkling in first-pass conventional spinning of hemispherical part

Flange wrinkling is one of the most common defects in conventional spinning. A lot of work has been done to find the reason for the flange wrinkling and the way to avoid it. However, the theoretical prediction of flange wrinkling is limited for the non-uniformly distributed stresses and complicated boundary conditions of the flange. In this paper, a FE (Finite element) model is established to study the deformation characteristic of the material in conventional spinning, two stable compressive stress rings distributed at the middle surface of the formed part are found, and the outer stress ring distributed at the flange is considered to be the key factor of flange wrinkling. A theoretical flange wrinkling prediction method is proposed based on the plastic buckling theory and the energy method with the boundary conditions extracted from the FE simulation results. Experiments are designed to research the flange wrinkling phenomenon and verify the proposed theoretical flange wrinkling prediction method. At last, effects of feed ratio on flange wrinkling are analyzed by this method, it is concluded that the decrease of the circumferential compressive stresses distributed in the flange caused by low feed ratio reduces the risk of flange wrinkling.

Shallow groundwater investigation using time-domain electromagnetic (TEM) method at Itay El-Baroud, Nile Delta, Egypt

The Nile Delta is one of the oldest known ancient delta, largest and most important depositional complex in the Mediterranean sedimentary basin. Furthermore, it is a unique site in Egypt that is suitable for accumulation and preservation of the Quaternary sediments. In this work we applied time-domain electromagnetic (TEM) method to investigate the Quaternary sediments sequence as well as detecting the groundwater aquifer in the area of study.A suite of 232 TEM sounding at 43 stations were carried out using a “SIROTEM MK-3” time-domain electromagnetic system. A simple coincident loop configuration, in which the same loop transmits and receives signals, was employed with loop side length of 25m. The 1-D modeling technique was applied to estimate the depth and the apparent resistivity of the interpreted geoelectrical data.Based on the interpretation of the acquired geophysical data, four geoelectric cross-sections were constructed. These sections show that the Upper Quaternary sequence consists of three geoelectric layers. The Holocene Nile mud is separated into two layers: the agricultural root zone (Layer 1) and thick water saturated mud (Layer 2). The Upper Pleistocene sandy aquifer (Layer 3) is very complicated non-linear boundary. This aquifer is the most important unit since it is considered as the main water bearing unit in the study area.

Unsteady three-dimensional MHD flow of a nano Eyring-Powell fluid past a convectively heated stretching sheet in the presence of thermal radiation, viscous dissipation and Joule heating

The purpose of this study is to investigate the unsteady magnetohydrodynamic three-dimensional flow induced by a stretching surface. An incompressible electrically conducting Eyring-Powell fluid fills the convectively heated stretching surface in the presence of nanoparticles. The effects of thermal radiation, viscous dissipation and Joule heating are accounted in heat transfer equation. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis. The highly nonlinear partial differential equations are reduced to ordinary differential equations with the help of similarity method. The reduced complicated two-point boundary value problem is treated numerically using Runge–Kutta–Fehlberg 45 method with shooting technique. A comparison of the obtained numerical results with existing results in a limiting sense is also presented. At the end, the effects of influential parameters on velocity, temperature and nanoparticles concentration fields are also discussed comprehensively. Further, the physical quantities of engineering interest such as the Nusselt number and Sherwood number are also calculated.

Strain hardening in 2D discrete dislocation dynamics simulations: A new ‘2.5D’ algorithm

The two-dimensional discrete dislocation dynamics (2D DD) method, consisting of parallel straight edge dislocations gliding on independent slip systems in a plane strain model of a crystal, is often used to study complicated boundary value problems in crystal plasticity. However, the absence of truly three dimensional mechanisms such as junction formation means that forest hardening cannot be modeled, unless additional so-called ‘2.5D’ constitutive rules are prescribed for short-range dislocation interactions. Here, results from three dimensional dislocation dynamics (3D DD) simulations in an FCC material are used to define new constitutive rules for short-range interactions and junction formation between dislocations on intersecting slip systems in 2D. The mutual strengthening effect of junctions on preexisting obstacles, such as precipitates or grain boundaries, is also accounted for in the model. The new ‘2.5D’ DD model, with no arbitrary adjustable parameters beyond those obtained from lower scale simulation methods, is shown to predict athermal hardening rates, differences in flow behavior for single and multiple slip, and latent hardening ratios. All these phenomena are well-established in the plasticity of crystals and quantitative results predicted by the model are in good agreement with experimental observations.

Similar Constructing Method for Solving the Boundary Value Problem of the Composite Thomson Equation

Based on the theory of similar structure of solution of the boundary value problem of differential equation, this paper studies the solution of a class of boundary value problem of the composite Thomson equation, After analysis? it is indicate that the solution with a form of continued fraction product is obtained by introducing functions of guide solution, constructing similar kernel functions and assembling coefficients of the left non-homogeneous boundary condition, functions of guide solution and similar kernel functions in this paper. Then a new method is obtained for solving the composite boundary value problem——Similar Constructive Method. Furthermore, the function solution is clearly illustrated by the chart which is carried out by the corresponding program in MTLAB. Thus, the method is not only simple and effective for solving the complicated boundary value problem of differential equation, but also is a kind of innovation of ideological.

Eulerian methods for high frequency acoustics

The high frequency approximation to the wave equation yields an eikonal equation for the wave phase and a transport equation for the amplitude. Unfortunately, straightforward computation of the eikonal equation poses a challenge in that solutions may be multivalued which affects the convergence of a numerical scheme. Traditional numerical schemes invoke ray tracing methods to solve the eikonal equation in a Lagrangian frame of reference. Ray tracing performs well in many cases and handles the multivalued solution inherently. However, in long range simulations or simulations with complicated boundary conditions, ray solutions may perform poorly as rays are very sensitive to small perturbations in initial conditions. In the past few decades, several methods for solving the eikonal equation in a fixed (Eulerian) frame of reference have been devised. As with any computational method, each has its own advantages and disadvantages, but it is useful to be aware of alternatives since many problems in physical acoustics may benefit from having phase solutions computed on a fixed grid. We present a brief review of recent Eulerian approaches and discuss the merits and open issues with each.

Lattice continuum and diffusional creep.

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

Procedure to Obtain Analytical Solutions of One-Dimensional Richards’ Equation for Infiltration in Two-Layered Soils

AbstractRichards’ equation (RE) constitutes the most used physically based formula for transient infiltration modeling in unsaturated soils, and it can be solved by using analytical or numerical procedures. Analytical methods require that certain assumptions should be made regarding the closed-form equations that are derived; if the assumptions can be considered reasonable, then the analytical procedures can represent a simple and practical tool (except some cases in which complicated boundary conditions could make the application of the methodology more difficult). Numerical methods do not have the strong limitations of available analytic procedures, and for this reason many numerical schemes are proposed in technical literature to solve RE. Nevertheless, numerical techniques could require high computational costs for application in large areas with respect to analytical procedures. For the frequent case of layered unsaturated soils, analytical solutions were derived by only imposing equal values of capi...

Study on how to resolve the boundary value problem of three-region composite Thomson equation

On the basis of the theory in similar structure of solution of the boundary value problem for a differential equation, this paper studies the boundary value problem of a three-region composite, Thomson equation. Firstly, this paper obtains similar structure related to solution of the boundary value problem of a three-region composite Thomson equation. Secondly, this paper points out the steps and flow chart about the algorithm for solving the boundary value problem. Finally, this paper gives an application of the obtained steps and draws the solution curve of the boundary value problem by executing the program on the computer. The obtained steps mentioned in this paper are not only simple and effective to resolve the complicated boundary value problem of a differential equation, but also useful to acquire the analytical solution of the model of composite reservoir.