Finite Difference Method Technique Research Articles

Inspection of thermal distribution through a porous fin of triangular profile with internal heat generation and electromagnetic field

The transient thermal analysis of a triangular profiled longitudinal porous fin with the combined effect of magnetic and electric fields is explained in this article. The heat transmission through the porous fin is modeled by a time-dependent nonlinear partial differential equation (PDE). The PDE and boundary conditions are transformed into a nonlinear dimensionless PDE with the aid of dimensionless terms. The numerical solution is obtained by using the technique of FDM (finite difference method). The consequences of non-dimensional thermoelectrical and thermomagnetic parameters, and other thermo-physical constraints including generation number, ambient temperature, radiation, and the convective parameter are also examined with the graphical explanations. The outcomes reveal that the emerging radiation, convective parameter, and dimensionless time parameter, faster the fin dissipate heat to the surrounding temperature. The presence of an electromagnetic field assists the triangular porous fin to distribute transient temperature effectively.

A numerical study of magneto‐double‐diffusive‐convection of Casson fluid over a vertical cone under nonuniform heating at surface of cone

AbstractThe objective of this investigation is to determine the impact of nonuniform heating on the transient natural convection of Casson fluid past a vertical cone in the appearance of a constant magnetic field. The overall analysis has executed in the presence of viscous dissipation, chemically reactive species, and ramped concentration. The derived governing partial differential equations in the dimensionless form are evaluated numerically using the implicit Crank‐Nicolson technique of finite difference method. The obtained numerical solutions for various physical parameters on all examined profiles have been shown graphically. The major result is found that the temperature and velocity profiles have a maximum magnitude at the middle of the lateral side of the cone. Also, the concentration profile has a maximum magnitude at for ramped concentration case.

Numerical modeling of a DBD in glow mode at atmospheric pressure

In this work, a fluid model of helium glow discharge at atmospheric pressure in a dielectric barrier discharge configuration has been developed and the discharge was numerically simulated. The transport equations for charged and excited species are self-consistent coupled to the Poisson equation for the electrical field calculation. A finite difference method technique is adopted; a detailed numerical procedure modeling is given. The addition of some nitrogen impurities to the helium successfully reproduced the discharge evolution during the breakdown. The numerical results showed that the discharge has a structure similar to DC low-pressure glow discharges and confirms the establishment of the glow regime at atmospheric pressure under very adequate conditions. The profiles of physical and electrical discharge parameters knowing that, particle densities, electric field, drift velocity, voltages and discharge current are presented and analyzed. A detailed study was made of the effect of nitrogen impurities on the stability of the glow mode of the discharge, and on the evolution of its parameters.

Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction–diffusion equations

In this article, two classes of finite difference methods are constructed to solve the space fractional semilinear delay reaction–diffusion equations. Firstly, fractional centered finite difference method in space and backward differential formula (BDF2) in time are employed to discrete the original equations. Secondly, the existence, uniqueness and convergence of the numerical method are analyzed at length by G-norm technique, and the convergence order is O(τ2+h2). Then the compact technique of finite difference method is used to further increase the accuracy in spatial direction, and a method with fourth accuracy in spatial dimension is obtained. The convergence orders are proved to be O(τ2+h4) in the sense of three classes of norms by GA-norm technique. Especially, we obtain the uniform convergence for the error estimation, which demonstrates competitive performance compared with the preceding work in the related references. Finally, two numerical examples are provided to verify our theoretical results and demonstrate the effectiveness of both methods when applied to simulate space fractional delay diffusive Nicholson’s blowflies equation.

SH-wave in a multilayered orthotropic crust under initial stress: A finite difference approach

The present work examines the finite difference modeling of SH-wave in a multilayered orthotropic crust to perceive the stability criterion and dispersion equation. The dispersion equation, for the case when (n-1) layers underlying the earth or along its surface, is obtained in a standard form. This paper actually assigns to apply the finite difference method in seismic wave propagation. The phase and group velocity are retrieved utilizing the techniques of finite difference method. For the occurrence of SH-wave propagation, stability conditions are constituted applying the technique of finite difference method in time and space. The graphs are produced to comprehend the concepts of dispersion equation, group velocity, and phase velocity.

A comparative study for lubrication of surface textured porous journal bearing with two different non-Newtonian fluid models

A study of two non-Newtonian fluid models viz., power law fluid model and couple stress fluid model on the hydrodynamic lubrication of porous journal bearing has been investigated. In addition, sinusoidal type of surface texturing is incorporated at different configurations on the bearing surface to find the performance of the bearing in both cases. The modified Reynolds equation with Darcy model using Reynolds boundary conditions is solved by central differencing technique of finite difference method. The bearing performance characteristics are calculated numerically and are compared with each other. A direct comparison between the two models has been shown graphically. The power law index (n) has taken in the range 1.0 to 1.2 while couple stress parameter (l*) has taken in the range 0 to 0.6. Numerical results show that both models significantly improve the load carrying capacity (W) and reduce coefficient of friction (COF). The results are more effective for low eccentricity ratios instead of high eccentricity ratios. It has also been observed for surface texturing that configuration 3 (72° to 144°) gives optimum results for both load carrying capacity as well as COF, when compared with all other configurations.

Sensitivity study with respect to direction of ADI method during re-flooding in AHWR

Abstract The Advanced Heavy water Reactor (AHWR) is a natural circulation vertical pressure tube type boiling light water cooled and heavy water moderated reactor. As the AHWR fuel bundle quenching under accident condition is designed primarily with radial jets at several axial locations, bottom re-flooding still remain open as another option. Radial direction injection of emergency core cooling leads to rewetting of AHWR fuel cluster in circumferential direction. A 3D fuel pin model has been developed by using Finite Difference Method (FDM) of transient heat conduction equation. Alternating Direction Implicit technique of Finite Difference Method (FDM) has been used for discretisation of numerical equation in different time step at different direction. Sensitivity numerical study with respect to direction of ADI method has been carried out to optimize the time step during the transient as well as steady state and is found that it is insensitivity with direction of solution. Further, to assess influence of circumferential rewetting vis-à-vis axial rewetting. Both the analyses are carried out with same fluid temperature and heat transfer coefficients as boundary conditions. It has been found from the analyses that for radial jet, the circumferential conduction is significant and overall the fuel temperature falls in the quench plane with the initiation of quenching event. The paper discusses the sensitivity study with respect to direction of ADI solution and comparison of numerical results for circumferential and axial rewetting for single pin.

Similitude Conditions Modeling Geosynthetic-Reinforced Piled Embankments Using FEM and FDM Techniques

The numerical modelling of geosynthetic-reinforced piled embankments using both the finite element method (FEM) and finite difference method (FDM) are compared. Plaxis 2D (FEM) was utilized to replicate FLAC (FDM) analysis originally presented by Han and Gabr on a unit cell axisymmetric model within a geosynthetic reinforced piled embankment (GRPE). The FEM and FED techniques were found to be in reasonable agreement, in both characteristic trend and absolute value. FEM consistently replicated the FDM outputs for deformational, loading, and load transfer mechanism (soil arching) response within the reinforced piled embankment structure with a reasonable degree of accuracy. However the FDM approach was found to give a slightly higher reinforcement tension and stress concentration but lower reinforcement strain at the pile cap than FEM, which was attributed to the greater discretize of the model geometry in the FDM than in FEM.

Numerical analysis for the thermophoretic coagulation of monodisperse particles at continuum regime

Coagulation is a process wherein aerosol particles collide with one another and adhere to form large particles in the system due to their relative motions. In this letter, we investigated thermophoretic coagulation of monodisperse aerosols on a constant temperature gradient between particles and gas molecules using a FDM (finite difference method) technique. The basic concept is to focus on a single particle attracting other particles considering their diffusional and thermophoretic motions to its collision surface. From the results of simulated particle flux, it shows that the thermophoretic coagulation is more effective for higher temperature gradient in the monodisperse aerosol particles.

Nonlinear Analysis of MEMS Electrostatic Microactuators: Primary and Secondary Resonances of the First Mode*

We use a discretization technique that combines the differential quadrature method (DQM) and the finite difference method (FDM) for the space and time, respectively, to study the dynamic behavior of a microbeam-based electrostatic microactuator. The adopted mathematical model based on the Euler— Bernoulli beam theory accounts for the system nonlinearities due to mid-plane stretching and electrostatic force. The nonlinear algebraic system obtained by the DQM—FDM is used to investigate the limit-cycle solutions of the microactuator. The stability of these solutions is ascertained using Floquet theory and/or long-time integration. The method is applied for large excitation amplitudes and large quality factors for primary and secondary resonances of the first mode in case of hardening-type and softening-type behaviors. We show that the combined DQM—FDM technique improves convergence of the dynamic solutions. We identify primary, subharmonic, and superharmonic resonances of the microactuator. We observe the occurrence of dynamic pull-in due to subharmonic and superharmonic resonances as the excitation amplitude is increased. Simultaneous resonances of the first and higher modes are identified for large orbits in both primary and secondary resonances.

A numerical model of infiltration processes for hysteretic flow coupled with mass conservation

AbstractThe study presents a numerical infiltration model of a hysteretic flow coupled with general mass conservation for practical application to unsaturated soil. In unsaturated soil, hysteresis is an important phenomenon in the complicated hydrological processes, and it is usually ignored when simulating the relationship of soil water content. The governing equation of unsaturated flow is the Richards equation, and it is difficult to obtain the analytic solutions because of the variation of temporal boundary conditions and the dynamics of change of soil water content in the vadose zone. The numerical solution is solved by the finite difference method technique with the Picard iteration scheme combined with the hysteresis model derived by Huang et al. (2005) and the mass conservation control within simulation domain. The results showed that the mixed form had better mass conservation. The present numerical solutions with the hysteresis model were verified by Gillham's experimental data of 1979. The results of the present mixed form numerical approximations with hysteresis effect are better than without hysteresis. In order to raise the accuracy of the soil water relationship numerical model, hysteresis and mass conservation are important factors in infiltration processes. Copyright © 2008 John Wiley & Sons, Ltd.

Ab initio calculations of the Ni K ‐edge XANES in Ni c Mg 1‐c O solid solutions

An interpretation of the Ni K-edge X-ray absorption near edge structure (XANES) in pure NiO and NicMg1-cO solid solutions is given based on three types of ab initio theoretical calculations: the full-multiple-scattering (FMS) approach, the finite difference method (FDM) and the full potential linear muffin-tin orbital (FP-LMTO) method within the LSDA+U approach. The first two methods differ in the cluster potential approximation: the spherically symmetric muffin-tin potential is used in the FMS approach, whereas a non-muffin-tin numerical potential makes the core of the FDM. We found that the FMS and FDM techniques allow rather accurate description of the experimental XANES signal especially above the absorption edge and produce close results, the FP-LMTO is more accurate close to the absorption edge. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Liquid vorticity computation in non-spherical bubble dynamics

The purpose of this work is to compare efficiency of a number of numerical techniques of computation of liquid vorticity from non-spherical bubble oscillations. The techniques based on the finite-difference method (FDM), the collocation method (one with differentiating (CMd) the integral boundary condition and another without it (CM)) and the Galerkin method (GM) have been considered. The central-difference approximations are used in FDM. Sinus functions are chosen as the basis in GM. Problems of decaying a small distortion of the spherical shape of a bubble and dynamics of a bubble under harmonic liquid pressure variation with various parameters are used for comparison. The FDM technique has been found to be most efficient in all the cases. Copyright © 2004 John Wiley & Sons, Ltd.

Modeling of graded-index channel waveguides using nonuniform finite difference method

A finite-difference method (FDM) with nonuniform discretization for the analysis of channel waveguides is presented. Application of the boundary conditions for either the quasi-TE or quasi-TM mode is illustrated. Flexible discretization of the grid structures minimizes memory size, resulting in much smaller computing time without sacrificing the accuracy of the solution. This nonuniform discretization FDM technique is used to model the well-guided small-mode-size Ti:LiNbO/sub 3/ waveguides. The model treats both finite and infinite source diffusion cases. Quasi-TM mode profiles and the corresponding eigenvalues are rigorously evaluated and the theoretical results agree very well with the experimental results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>