Difference Method In Order Research Articles

Design of Underground Pipelines under Arbitrary Seismic Loading

On the basis of Hamilton-Ostrogradskiy variation principle a system of equations of linear pipeline vibrations interacting with surrounding soil is derived with appropriate boundary and initial conditions under arbitrary direction of seismic effect. Dynamic problem of underground pipeline is solved by finite difference method of the second order of accuracy with different combinations of boundary conditions under the effect of seismic load on a given law with arbitrary direction. Numerical implementation of the problem is realized.

High accuracy non-polynomial spline in compression method for one-space dimensional quasi-linear hyperbolic equations with significant first order space derivative term

In this paper, we propose a new three-level implicit nine point compact non-polynomial spline in compression finite difference method of order two in time and four in space directions, based on non-polynomial spline approximation in x-direction and central difference approximation in t-direction for the numerical solution of one-space dimensional second order quasi-linear hyperbolic partial differential equations with first order space derivative term. We describe the mathematical details of the method and also discuss how our method is able to handle wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is shown to be unconditionally stable. Numerical results are provided to justify the usefulness of the proposed method.

A Novel Method for Detecting Abnormal Energy Data in Building Energy Monitoring System

This paper presents a novel abnormal data detecting algorithm based on the first order difference method, which could be used to find out outlier in building energy consumption platform real time. The principle and criterion of methodology are discussed in detail. The results show that outlier in cumulative power consumption could be detected by our method.

Remote sensing retrieval for chlorophyll-a concentration in seasonal turbid case II water based on baseline correction of spectra

Chlorophyll-a( Chl. a) concentration is an important indicator of water quality evaluation,which is affected by the seasonal changes of suspended matter concentration. How to weaken the spectral interferences of suspended matter is an important issue in the retrieval of Chl. a concentrations with remote sensing in inland water. Based on six field surveys in 2011-2013 in Guishui River,the inversion ability of Chl. a concentrations with three-band model and support vector regression model were evaluated,in which baseline correction and first order differential method were used to weaken the spectral noises. Reflectance of 750 nm was defined as a baseline,a connecting line of reflectance from 500 nm to 750 nm was defined as another baseline. Baseline correction was defined as spectral reflectance minus baseline values. The validation was performed using data of samples in July 2013,the results demonstrated that SVR model was better than the three-band model in reversion of the Chl. a concentration in seasonal turbid water. Band reflectance combinations after baseline correction screening as the input variables can improve the inversion accuracy of the SVR estimation model. The determination coefficient was 0. 68 and the root mean square error was 3. 38 μg / L. Linear baseline correction can slightly improve the inversion accuracy of the three- band model.

Solving the Poisson Equation by an Interval Difference Method of the Second Order

The paper deals with an interval difference method for solving the Poisson equation based on the conventional central-difference method. We present the interval method in full details. The method is constructed in such a way that the exact solution is included in the interval solution obtained. Some numerical results obtained in floating-point interval arithmetic are also presented.

Comparison study of differential transform method with finite difference method for magnetoconvection in a vertical channel

In this paper, coupled nonlinear equations governing the flow for magnetoconvection in a vertical channel for open and short circuits are solved. The calculations are carried out by using differential transformation method (DTM) which is a semi-numerical–analytical solution technique. By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related initial conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced, and then applied for the aforementioned problems. The current results are then compared with those derived from the finite difference method (FDM) and perturbation method (PM) in order to verify the accuracy of the proposed method. The findings reveal that the DTM can achieve more suitable results in predicting the solution of such problems. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21035

A sixth-order compact finite difference method for non-classical vibration analysis of nanobeams including surface stress effects

A non-classical model for the free vibrations of nanobeams accounting for surface stress effects is developed in this study. Based on Gurtin–Murdoch elasticity theory, the influence of surface stress is incorporated into the Euler–Bernoulli beam theory. A compact finite difference method (CFDM) of sixth order is employed for discretizing the non-classical governing differential equation to obtain the natural frequencies of nanobeams subject to different boundary conditions. To check the validity of the present numerical solution, based on an exact solution, an explicit formula for the fundamental frequency of simply-supported nanobeams is obtained. Good agreement between the results of exact and numerical solutions is achieved, confirming the validity and accuracy of the present numerical scheme. The comparison between the results generated by CFDM with those obtained by the conventional finite difference method (FDM) further reveals the advantages of the compact method over its classical counterpart. The influences of beam thickness, surface density, surface residual stress, surface elastic constants, and boundary conditions on the natural frequencies of nanobeams are also investigated. It is indicated that the effect of surface stress on the vibrational response of a nanobeam is dependent on its aspect ratio and thickness.

Modeling of Automatic Power Output Prediction for Wind Mechanical Generator

Due to the instability of the output in wind power, there exists some difficulties on wind power merger to electricity grid. The fast forecasting of output of wind power is in favor of reasonable allocation system and increase the possibility of power merger in a large scale. Based on the actual wind power data, this article utilizes the one order differential method to remove data unsteady and obtains the stable data. In view of the ARMA time series, a numerical prediction model of wind power output is established. The results show that the model has good precision and can be used in the production practice.

Software metamaterials: Transformation media based multiscale techniques for computational electromagnetics

This paper presents computational models employing special transformation-based media—which we call software metamaterials—for the purpose of enhancing the ability of numerical modeling methods for solving multi-scale electromagnetic boundary value problems involving features with multiple length or frequency scales or both. The multi-scale problems, in general, suffer from difficulties in mesh generation and the number of unknowns due to certain meshing requirements dictated by the fine features of the problem. The underlying idea in this study is to introduce transformation media into the computational domain of the finite element method (or finite difference methods) in order to allow uniform and easy-to-generate meshes by avoiding mesh refinement, and therefore, to develop efficient and simple computer-aided simulation tools. In other words, a virtual equivalent problem is created, which acts like the original problem. The techniques proposed in this paper are validated via several finite element simulations in the context of TMz electromagnetic scattering problems.

Grid stabilization of high-order one-sided differencing II: Second-order wave equations

We demonstrate the stable boundary closure of difference methods of order up through 16 for the solution of wave equations in second order form. Our method combines the introduction of 1–2 judiciously placed subcell grid points near the boundary with minimal-stencil, one-sided difference operators of the same order as the interior scheme. The method is tested on a variety of problems including the scalar wave equation discretized on mapped grids and overlapping composite grids, as well as an integrable nonlinear system.

SIMULATION OF VORTEX STRUCTURE IN SUPERSONIC FREE SHEAR LAYER USING PSE METHOD

The method of parabolized stability equations (PSE) are applied in the analysis of nonlinear stability and the simulation of flow structure in supersonic free shear layer. High accuracy numerical techniques including self-similar basic flow, high order differential method, appropriate transformation and decomposition of nonlinear terms are adopted and developed to solve the PSE effectively for free shear layer. The spatial evolving unstable waves which dominate the flow structure are investigated through nonlinear coupling spatial marching methods. The nonlinear interactions between harmonic waves are further analyzed and instantaneous flow field are obtained by adding the harmonic waves into basic flow. Relevant data agree well with that of DNS. The results demonstrate that T-S wave does not keeping growing exponential as the linear evolution, the energy transfer to high order harmonic modes and finally all harmonic modes get saturation due to the nonlinear interaction; Mean flow distortion is produced by the nonlinear interaction between the harmonic and its conjugate harmonic, makes great change to the average flow and increases the thickness of shear layer; PSE methods can well capture the large scale nonlinear flow structure in the supersonic free shear layer such as vortex roll-up, vortex pairing and nonlinear saturation.

Numerical Solution of Second-Order Linear Fredholm Integro-Differential Equation Using Generalized Minimal Residual Method

Problem statement: This research purposely brought up to solve complicated equations such as partial differential equations, integral equations, Integro-Differential Equations (IDE), stochastic equations and others. Many physical phenomena contain mathematical formulations such integro-differential equations which are arise in fluid dynamics, biological models and chemical kinetics. In fact, several formulations and numerical solutions of the linear Fredholm integro-differential equation of second order currently have been proposed. This study presented the numerical solution of the linear Fredholm integro-differential equation of second order discretized by using finite difference and trapezoidal methods. Approach: The linear Fredholm integro-differential equation of second order will be discretized by using finite difference and trapezoidal methods in order to derive an approximation equation. Later this approximation equation will be used to generate a dense linear system and solved by using the Generalized Minimal Residual (GMRES) method. Results: Several numerical experiments were conducted to examine the efficiency of GMRES method for solving linear system generated from the discretization of linear Fredholm integro-differential equation. For the comparison purpose, there are three parameters such as number of iterations, computational time and absolute error will be considered. Based on observation of numerical results, it can be seen that the number of iterations and computational time of GMRES have declined much faster than Gauss-Seidel (GS) method. Conclusion: The efficiency of GMRES based on the proposed discretization is superior as compared to GS iterative method.

A compact difference scheme for the fractional diffusion-wave equation

This article is devoted to the study of high order difference methods for the fractional diffusion-wave equation. The time fractional derivatives are described in the Caputo’s sense. A compact difference scheme is presented and analyzed. It is shown that the difference scheme is unconditionally convergent and stable in L ∞ -norm. The convergence order is O ( τ 3 - α + h 4 ) . Two numerical examples are also given to demonstrate the theoretical results.

Numerical Simulation and Experimental Analysis of Laser Surface Remelting of AISI 304 Stainless Steel Samples

The aim of this work is to develop a heat transfer mathematical model based on the finite difference method in order to simulate temperature fields in the laser surface remelting process. Convective heat transfer in the remelted pool is taken into account by using the effective thermal conductivity approach. Experiments of laser surface remelting of AISI 304 austenitic stainless steel samples were carried out in the present investigation, and numerical simulations were applied for the CO2 laser machine operating parameters. The work also encompasses the analysis of microstructural and microhardness variations throughout the resulting treated and unmolten zones. This study permits to conclude that numerical simulation is a useful tool in setting the laser operating parameters, enabling pre-programming of the extent of the treated area.

Numerical and experimental analysis of rapidly solidified laser remelted Al 5wt pct Ni surfaces

The aim of this work was to develop a heat transfer mathematical model based on the finite difference method in order to simulate temperature fields in the laser surface remelting process. Convective heat transfer in the remelted pool was taken into account by using the effective thermal conductivity approach. Theoretical predictions furnished by previous models from the literature were used for validation of numerical simulations performed with the proposed model. Experiments of laser surface remelting of Al-5 wt pct Ni samples were carried out in the present investigation, and numerical simulations were applied for the laser machine operating parameters. The work also encompasses an analysis of microstructural and microhardness variations throughout the resulting treated and untreated zones.

Numerical Simulation and Experimental Analysis of Laser Surface Remelting of AISI 420 Stainless Steel Samples

The aim of this work is to develop a heat transfer mathematical model based on the finite difference method in order to simulate temperature fields in the laser surface remelting process. Convective heat transfer in the remelted pool is taken into account by using the effective thermal conductivity approach. Experiments of laser surface remelting of AISI 420 stainless steel samples were carried out in the present investigation, and numerical simulations were applied for the laser machine operating parameters. The work also encompasses the analysis of microstructural and microhardness variations throughout the resulting treated and unmolten zones.

3D thermal model to investigate component displacement phenomenon during reflow soldering

This paper reports the development of a 3D component-level thermal model to investigate the displacement of the components during the reflow soldering process. One of the root causes of displacement is the temperature deviation between the contact surfaces of the components. Therefore, our model examines the temperature distribution at the level of discrete components and not at the level of whole assembly as is the case of general models used in reflow soldering [Whalley DC. A simplified reflow soldering process model. J Mater Process Technol 2004;150:134–44; Sarvar F, Conway PP. Effective modelling of the reflow soldering process: basis construction and operation of a process model. IEEE Trans Compon Pack Manuf Technol C: Manuf 1998;21(2):126–33; Inoue M, Koyanagawa T. Thermal simulation for predicting substrate temperature during reflow soldering process. In: IEEE Proceeding of the 55th ECTC; 2005. p. 1021–6]. Our model is based on the thermal or central node theory. This means that the investigated area is divided into thermal cells representing the thermal behaviour of the given material. During the model discretization a nonuniform cuboid cell grid is used, with this the resolution of the model can be refined to focus on areas of interest (e.g. the soldering pads) whilst reducing the involvement with the less important areas (such as the epoxy body of a component). This approach therefore allows to achieve a significant increase of spatial resolution of the calculated temperature distribution in some distinct areas with only a little increase of model complexity. The model is described by common heat conduction and convection equations and these are solved by the finite difference method in order to achieve high calculation speeds and easy implementation. The ability of our single purpose model is then compared with a general purpose FEM analyzer. It results that the calculation accuracy of our model is comparable with more detailed models. Also, its calculation speed and application is much faster and easier.

Numerical and Experimental Analysis of Laser Surface Remelting of Al 9wt% Si Alloy Samples

Laser materials processing has been widely applied in industrial processes due to unique precision and very localized thermal action furnished by the laser’s high energy density and power controllability. With the inherent rapid heating and cooling rates to which this surface layer is subjected, this process provides an opportunity to produce different microstructures from that of the bulk metal leading to useful properties. The aim of this work is to develop a heat transfer mathematical model based on the finite difference method in order to simulate temperature fields in the laser surface remelting process. Convective heat transfer in the remelted pool is taken into account by using the effective thermal conductivity approach. Theoretical predictions furnished by previous models from the literature were used for validation of numerical simulations performed with the proposed model. Experiments of laser surface remelting of Al-9 wt pct Si samples was carried out in the present investigation, and numerical simulations was applied for the laser machine operating parameters. The work also encompasses the analysis of microstructural and microhardness variations throughout the resulting treated and unmolten zones.

A FINITE DIFFERENCE METHOD FOR PIECEWISE DETERMINISTIC PROCESSES WITH MEMORY

In this paper the numerical approximation of solutions of Liouville‐Master Equation for time‐dependent distribution functions of Piecewise Deterministic Processes with memory is considered. These equations are linear hyperbolic PDEs with non‐constant coefficients, and boundary conditions that depend on integrals over the interior of the integration domain. We construct a finite difference method of the first order, by a combination of the upwind method, for PDEs, and by a direct quadrature, for the boundary condition. We analyse convergence of the numerical solution for distribution functions evolving towards an equilibrium. Numerical results for two problems, whose analytical solutions are known in closed form, illustrate the theoretical finding.

Weak approximations of solutions of a first order hyperbolic stochastic partial differential equation

The present article focuses on the use of difference methods in order to approximate the solutions of stochastic partial differential equations of Itô type, in particular hyperbolic equations. We develop the main notions of deterministic difference methods, i.e. convergence, consistency and stability for the stochastic case. We prove a stochastic version of Lax-Richtmyer theorem giving the existence of a weak convergent subsequence of the approximating scheme if the scheme is both consistent and stable.