Abstract: A numerical solution of the initial boundary value
problem of the suspended string vibrating equation with the
particular nonlinear damping term based on the finite difference
scheme is presented in this paper. The investigation of how the
second and third power terms of the nonlinear term affect the
vibration characteristic. We compare the vibration amplitude as a
result of the third power nonlinear damping with the second power
obtained from previous report provided that the same initial shape
and initial velocities are assumed. The comparison results show that
the vibration amplitude is inversely proportional to the coefficient of
the damping term for the third power nonlinear damping case, while
the vibration amplitude is proportional to the coefficient of the
damping term in the second power nonlinear damping case.
Abstract: An efficient transient flow simulation for gas
pipelines and networks is presented. The proposed transient flow
simulation is based on the transfer function models and MATLABSimulink.
The equivalent transfer functions of the nonlinear
governing equations are derived for different types of the boundary
conditions. Next, a MATLAB-Simulink library is developed and
proposed considering any boundary condition type. To verify the
accuracy and the computational efficiency of the proposed
simulation, the results obtained are compared with those of the
conventional finite difference schemes (such as TVD, method of
lines, and other finite difference implicit and explicit schemes). The
effects of the flow inertia and the pipeline inclination are
incorporated in this simulation. It is shown that the proposed
simulation has a sufficient accuracy and it is computationally more
efficient than the other methods.
Abstract: In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.
Abstract: A compact 1x3 power splitter based on Photonic
Crystal Waveguides (PCW) with flexible power splitting ratio is
presented in this paper. Multimode interference coupler (MMI) is
integrated with PCW. The device size reduction compared with the
conventional MMI power splitter is attributed to the large dispersion
of the PCW. Band Solve tool is used to calculate the band structure of
PCW. Finite Difference Time Domain (FDTD) method is adopted to
simulate the relevant structure at 1550nm wavelength. The device is
polarization insensitive and allows the control of output (o/p) powers
within certain percentage points for both polarizations.
Abstract: For fire safety purposes, the fire resistance and the
structural behavior of reinforced concrete members are assessed to
satisfy specific fire performance criteria. The available prescribed
provisions are based on standard fire load. Under various fire
scenarios, engineers are in need of both heat transfer analysis and
structural analysis. For heat transfer analysis, the study proposed a
modified finite difference method to evaluate the temperature profile
within a cross section. The research conducted is limited to concrete
sections exposed to a fire on their one side. The method is based on
the energy conservation principle and a pre-determined power
function of the temperature profile. The power value of 2.7 is found
to be a suitable value for concrete sections. The temperature profiles
of the proposed method are only slightly deviate from those of the
experiment, the FEM and the FDM for various fire loads such as
ASTM E 119, ASTM 1529, BS EN 1991-1-2 and 550 oC. The
proposed method is useful to avoid incontinence of the large matrix
system of the typical finite difference method to solve the
temperature profile. Furthermore, design engineers can simply apply
the proposed method in regular spreadsheet software.
Abstract: Few studies have been conducted on polymeric strip
and the behavior of soil retaining walls. This paper will present the
effect of frequency on the dynamic behavior of reinforced soil
retaining walls with polymeric strips. The frequency content
describes how the amplitude of a ground motion is distributed among
different frequencies. Since the frequency content of an earthquake
motion will strongly influence the effects of that motion, the
characterization of the motion cannot be completed without the
consideration of its frequency content. The maximum axial force of
reinforcements and horizontal displacement of the reinforced walls
are focused in this research. To clarify the dynamic behavior of
reinforced soil retaining walls with polymeric strips, a numerical
modeling using Finite Difference Method is benefited. As the results
indicate, the frequency of input base acceleration has an important
effect on the behavior of these structures. Because of resonant in the
system, where the frequency of the input dynamic load is equal to the
natural frequency of the system, the maximum horizontal
displacement and the maximum axial forces in polymeric strips is
occurred. Moreover, they were to increase the structure flexibility
because of the main advantages of polymeric strips; i.e. being simple
method of construction, having a homogeneous behavior with soils,
and possessing long durability, which are of great importance in
dynamic analysis.
Abstract: The aim of this paper is to study the internal
stabilization of the Bernoulli-Euler equation numerically. For this,
we consider a square plate subjected to a feedback/damping force
distributed only in a subdomain. An algorithm for obtaining an
approximate solution to this problem was proposed and implemented.
The numerical method used was the Finite Difference Method.
Numerical simulations were performed and showed the behavior of
the solution, confirming the theoretical results that have already been
proved in the literature. In addition, we studied the validation of the
numerical scheme proposed, followed by an analysis of the numerical
error; and we conducted a study on the decay of the energy associated.
Abstract: Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.
Abstract: The present study investigates numerically the
phenomenon of vortex-shedding and its suppression in twodimensional
mixed convective flow past a square cylinder under the
joint influence of buoyancy and free-stream orientation with respect
to gravity. The numerical experiments have been conducted at a
fixed Reynolds number (Re) of 100 and Prandtl number (Pr) of 0.71,
while Richardson number (Ri) is varied from 0 to 1.6 and freestream
orientation, α, is kept in the range 0o≤ α ≤ 90o, with 0o
corresponding to an upward flow and 90o representing a cross-flow
scenario, respectively. The continuity, momentum and energy
equations, subject to Boussinesq approximation, are discretized using
a finite difference method and are solved by a semi-explicit pressure
correction scheme. The critical Richardson number, leading to the
suppression of the vortex-shedding (Ric), is estimated by using
Stuart-Landau theory at various free-stream orientations and the
neutral curve is obtained in the Ri-α plane. The neutral curve
exhibits an interesting non-monotonic behavior with Ric first
increasing with increasing values of α upto 45o and then decreasing
till 70o. Beyond 70o, the neutral curve again exhibits a sharp
increasing asymptotic trend with Ric approaching very large values
as α approaches 90o. The suppression of vortex shedding is not
observed at α = 90o (cross-flow). In the unsteady flow regime, the
Strouhal number (St) increases with the increase in Richardson
number.
Abstract: Artificial atoms are growing fields of interest due to their physical and optoelectronicapplications. The absorption spectra of the proposed artificial atom inpresence of Tera-Hertz field is investigated theoretically. We use the non-perturbativeFloquet theory and finite difference method to study the electronic structure of ArtificialAtom. The effect of static electric field on the energy levels of artificial atom is studied.The effect of orientation of static electric field on energy levels and diploe matrix elementsis also highlighted.
Abstract: Flow movement in unsaturated soil can be expressed
by a partial differential equation, named Richards equation. The
objective of this study is the finding of an appropriate implicit
numerical solution for head based Richards equation. Some of the
well known finite difference schemes (fully implicit, Crank Nicolson
and Runge-Kutta) have been utilized in this study. In addition, the
effects of different approximations of moisture capacity function,
convergence criteria and time stepping methods were evaluated. Two
different infiltration problems were solved to investigate the
performance of different schemes. These problems include of vertical
water flow in a wet and very dry soils. The numerical solutions of
two problems were compared using four evaluation criteria and the
results of comparisons showed that fully implicit scheme is better
than the other schemes. In addition, utilizing of standard chord slope
method for approximation of moisture capacity function, automatic
time stepping method and difference between two successive
iterations as convergence criterion in the fully implicit scheme can
lead to better and more reliable results for simulation of fluid
movement in different unsaturated soils.
Abstract: In this paper, we have proposed two novel plasmonic demultiplexing structures based on metal-insulator-metal surfaces which, beside their compact size, have a very good transmission spectrum. The impact of the key internal parameters on the transmission spectrum is numerically analyzed by using the twodimensional (2D) finite difference time domain (FDTD) method. The proposed structures could be used to develop ultra-compact photonic wavelength demultiplexing devices for large-scale photonic integration.
Abstract: A novel PDE solver using the multidimensional wave
digital filtering (MDWDF) technique to achieve the solution of a 2D
seismic wave system is presented. In essence, the continuous physical
system served by a linear Kirchhoff circuit is transformed to an
equivalent discrete dynamic system implemented by a MD wave
digital filtering (MDWDF) circuit. This amounts to numerically
approximating the differential equations used to describe elements of a
MD passive electronic circuit by a grid-based difference equations
implemented by the so-called state quantities within the passive
MDWDF circuit. So the digital model can track the wave field on a
dense 3D grid of points. Details about how to transform the continuous
system into a desired discrete passive system are addressed. In
addition, initial and boundary conditions are properly embedded into
the MDWDF circuit in terms of state quantities. Graphic results have
clearly demonstrated some physical effects of seismic wave (P-wave
and S–wave) propagation including radiation, reflection, and
refraction from and across the hard boundaries. Comparison between
the MDWDF technique and the finite difference time domain (FDTD)
approach is also made in terms of the computational efficiency.
Abstract: Subgrade moisture content varies with environmental and soil conditions and has significant influence on pavement performance. Therefore, it is important to establish realistic estimates of expected subgrade moisture contents to account for the effects of this variable on predicted pavement performance during the design stage properly. The initial boundary soil suction profile for a given pavement is a critical factor in determining expected moisture variations in the subgrade for given pavement and climatic and soil conditions. Several numerical models have been developed for predicting water and solute transport in saturated and unsaturated subgrade soils. Soil hydraulic properties are required for quantitatively describing water and chemical transport processes in soils by the numerical models. The required hydraulic properties are hydraulic conductivity, water diffusivity, and specific water capacity. The objective of this paper was to determine isothermal moisture profiles in a soil fill and predict the soil moisture movement above the ground water table using a simple one-dimensional finite difference model.
Abstract: In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.
Abstract: This paper adopted the hybrid differential transform approach for studying heat transfer problems in a gold/chromium thin film with an ultra-short-pulsed laser beam projecting on the gold side. The physical system, formulated based on the hyperbolic two-step heat transfer model, covers three characteristics: (i) coupling effects between the electron/lattice systems, (ii) thermal wave propagation in metals, and (iii) radiation effects along the interface. The differential transform method is used to transfer the governing equations in the time domain into the spectrum equations, which is further discretized in the space domain by the finite difference method. The results, obtained through a recursive process, show that the electron temperature in the gold film can rise up to several thousand degrees before its electron/lattice systems reach equilibrium at only several hundred degrees. The electron and lattice temperatures in the chromium film are much lower than those in the gold film.
Abstract: Numerical investigation of the characteristics of an 80°
delta wing in combined force-pitch and free-roll is presented. The
implicit, upwind, flux-difference splitting, finite volume scheme and
the second-order-accurate finite difference scheme are employed to
solve the flow governing equations and Euler rigid-body dynamics
equations, respectively. The characteristics of the delta wing in
combined free-roll and large amplitude force-pitch is obtained
numerically and shows a well agreement with experimental data
qualitatively. The motion in combined force-pitch and free-roll
significantly reduces the lift force and transverse stabilities of the delta
wing, which is closely related to the flying safety. Investigations on
sensitive factors indicate that the roll-axis moment of inertia and the
structural damping have great influence on the frequency and
amplitude, respectively. Moreover, the turbulence model is considered
as an influencing factor in the investigation.
Abstract: In a previous work, we presented the numerical
solution of the two dimensional second order telegraph partial
differential equation discretized by the centred and rotated five-point
finite difference discretizations, namely the explicit group (EG) and
explicit decoupled group (EDG) iterative methods, respectively. In
this paper, we utilize a domain decomposition algorithm on these
group schemes to divide the tasks involved in solving the same
equation. The objective of this study is to describe the development
of the parallel group iterative schemes under OpenMP programming
environment as a way to reduce the computational costs of the
solution processes using multicore technologies. A detailed
performance analysis of the parallel implementations of points and
group iterative schemes will be reported and discussed.
Abstract: Photonic Crystal (PhC) based devices are being
increasingly used in multifunctional, compact devices in integrated
optical communication systems. They provide excellent
controllability of light, yet maintaining the small size required for
miniaturization. In this paper, the band gap properties of PhCs and
their typical applications in optical waveguiding are considered.
Novel PhC based applications such as nonlinear switching and
tapers are considered and simulation results are shown using the
accurate time-domain numerical method based on Finite Difference
Time Domain (FDTD) scheme. The suitability of these devices for
novel applications is discussed and evaluated.
Abstract: Water pollution assessment problems arise frequently
in environmental science. In this research, a finite difference method
for solving the one-dimensional steady convection-diffusion equation
with variable coefficients is proposed; it is then used to optimize
water treatment costs.