Abstract: In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function ψ (x,y)and the function φ (x,y)as independent variables where for irrotational flow φ (x,y)can be recognized as the velocity potential function, for rotational flow φ (x,y)ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on the finite difference scheme on a uniform mesh is employed. The technique described is capable of tackling the so-called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct geometries. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists.
Abstract: In this paper, the application of the Mode Matching
(MM) method in the case of photonic crystal waveguide
discontinuities is presented. The structure under consideration is
divided into a number of cells, which supports a number of guided
and evanescent modes. These modes can be calculated numerically
by an alternative formulation of the plane wave expansion method
for each frequency. A matrix equation is then formed relating the
modal amplitudes at the beginning and at the end of the structure.
The theory is highly efficient and accurate and can be applied to
study the transmission sensitivity of photonic crystal devices due to
fabrication tolerances. The accuracy of the MM method is compared
to the Finite Difference Frequency Domain (FDFD) and the Adjoint
Variable Method (AVM) and good agreement is observed.
Abstract: Geosynthetics have proved to be suitable for
reinforced soil retaining walls. Based on the increasing uses of
geosynthetic reinforced soil systems in the regions, which bear
frequent earthquakes, the study of dynamic behavior of structures
seems necessary. Determining the reinforcement forces is; therefore,
one of the most important and main points of discussions in
designing retaining walls, by which we prevent from conservative
planning. Thus, this paper intended to investigate the effects of such
parameters as wall height, acceleration type, vertical spacing of
reinforcement, type of reinforcement and soil type on forces and
deformation through numerical modeling of the geosynthetic
reinforced soil retaining walls (GRSRW) under dynamic loading with
finite difference method by using FLAC. The findings indicate rather
positive results with each parameter.
Abstract: This paper presents the development of an active
vibration control using direct adaptive controller to suppress the
vibration of a flexible beam system. The controller is realized based
on linear parametric form. Differential evolution optimisation
algorithm is used to optimize the controller using single objective
function by minimizing the mean square error of the observed
vibration signal. Furthermore, an alternative approach is developed to
systematically search for the best controller model structure together
with it parameter values. The performance of the control scheme is
presented and analysed in both time and frequency domain.
Simulation results demonstrate that the proposed scheme is able to
suppress the unwanted vibration effectively.
Abstract: A numerical analysis used to simulate the effects of wavy surfaces and thermal radiation on natural convection heat transfer boundary layer flow over an inclined wavy plate has been investigated. A simple coordinate transformation is employed to transform the complex wavy surface into a flat plate. The boundary layer equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the Gauss-Seidel algorithm with relaxation coefficient. Effects of the wavy geometry, the inclination angle of the wavy plate and the thermal radiation on the velocity profiles, temperature profiles and the local Nusselt number are presented and discussed in detail.
Abstract: A simple model for studying convectional lifting
processes in the tropics is described in this paper with some tests of
the model in dry air. The model consists of the density equation, the
wind equation, the vertical velocity equation, and the temperature
equation. The model domain is two-dimensional with length 100 km
and height 17.5 km. Plan for experiments to investigate the effects of
the heating surface, the deep convection approximation and the
treatment of velocities at the boundaries are discussed. Equations for
the simplified treatment of moisture in the atmosphere in future
numerical experiments are also given.
Abstract: In this paper, fully developed flow and heat transfer of
viscoelastic materials in curved ducts with square cross section under
constant heat flux have been investigated. Here, staggered mesh is
used as computational grids and flow and heat transfer parameters
have been allocated in this mesh with marker and cell method.
Numerical solution of governing equations has being performed with
FTCS finite difference method. Furthermore, Criminale-Eriksen-
Filbey (CEF) constitutive equation has being used as viscoelastic
model. CEF constitutive equation is a suitable model for studying
steady shear flow of viscoelastic materials which is able to model
both effects of the first and second normal stress differences. Here, it
is shown that the first and second normal stresses differences have
noticeable and inverse effect on secondary flows intensity and mean
Nusselt number which is the main novelty of current research.
Abstract: Electromagnetic flow meter by measuring the varying of magnetic flux, which is related to the velocity of conductive flow, can measure the rate of fluids very carefully and precisely. Electromagnetic flow meter operation is based on famous Faraday's second Law. In these equipments, the constant magnetostatic field is produced by electromagnet (winding around the tube) outside of pipe and inducting voltage that is due to conductive liquid flow is measured by electrodes located on two end side of the pipe wall. In this research, we consider to 2-dimensional mathematical model that can be solved by numerical finite difference (FD) solution approach to calculate induction potential between electrodes. The fundamental concept to design the electromagnetic flow meter, exciting winding and simulations are come out by using MATLAB and PDE-Tool software. In the last stage, simulations results will be shown for improvement and accuracy of technical provision.
Abstract: Several numerical schemes utilizing central difference
approximations have been developed to solve the Goursat problem.
However, in a recent years compact discretization methods which
leads to high-order finite difference schemes have been used since it
is capable of achieving better accuracy as well as preserving certain
features of the equation e.g. linearity. The basic idea of the new
scheme is to find the compact approximations to the derivative terms
by differentiating centrally the governing equations. Our primary
interest is to study the performance of the new scheme when applied
to two Goursat partial differential equations against the traditional
finite difference scheme.
Abstract: The objective of this paper is to analyse the
application of the Half-Sweep Gauss-Seidel (HSGS) method by using
the Half-sweep approximation equation based on central difference
(CD) and repeated trapezoidal (RT) formulas to solve linear fredholm
integro-differential equations of first order. The formulation and
implementation of the Full-Sweep Gauss-Seidel (FSGS) and Half-
Sweep Gauss-Seidel (HSGS) methods are also presented. The HSGS
method has been shown to rapid compared to the FSGS methods.
Some numerical tests were illustrated to show that the HSGS method
is superior to the FSGS method.
Abstract: The spectral action balance equation is an equation that
used to simulate short-crested wind-generated waves in shallow water
areas such as coastal regions and inland waters. This equation consists
of two spatial dimensions, wave direction, and wave frequency which
can be solved by finite difference method. When this equation with
dominating convection term are discretized using central differences,
stability problems occur when the grid spacing is chosen too coarse.
In this paper, we introduce the splitting upwind schemes for avoiding
stability problems and prove that it is consistent to the upwind scheme
with same accuracy. The splitting upwind schemes was adopted
to split the wave spectral action balance equation into four onedimensional
problems, which for each small problem obtains the
independently tridiagonal linear systems. For each smaller system
can be solved by direct or iterative methods at the same time which
is very fast when performed by a multi-processor computer.
Abstract: The stability characteristics of water lubricated journal bearings having three axial grooves are obtained theoretically. In this lubricant (water) is fed under pressure from one end of the bearing, through the 3-axial grooves (groove angles may vary). These bearings can use the process fluid as the lubricant, as in the case of feed water pumps. The Reynolds equation is solved numerically by the finite difference method satisfying the boundary conditions. The stiffness and damping coefficient for various bearing number and eccentricity ratios, assuming linear pressure drop along the groove, shows that smaller groove angles better results.
Abstract: In this paper, the difference between the Alternating
Direction Method (ADM) and the Non-Splitting Method (NSM) is
investigated, while both methods applied to the simulations for 2-D
multimaterial radiation diffusion issues. Although the ADM have the
same accuracy orders with the NSM on the uniform meshes, the
accuracy of ADM will decrease on the distorted meshes or the
boundary of domain. Numerical experiments are carried out to
confirm the theoretical predication.
Abstract: The main objective of the present paper is to derive an easy numerical technique for the analysis of the free vibration through the stepped regions of plates. Based on the utilities of the step by step integration initial values IV and Finite differences FD methods, the present improved Initial Value Finite Differences (IVFD) technique is achieved. The first initial conditions are formulated in convenient forms for the step by step integrations while the upper and lower edge conditions are expressed in finite difference modes. Also compatibility conditions are created due to the sudden variation of plate thickness. The present method (IVFD) is applied to solve the fourth order partial differential equation of motion for stepped plate across two different panels under the sudden step compatibility in addition to different types of end conditions. The obtained results are examined and the validity of the present method is proved showing excellent efficiency and rapid convergence.
Abstract: A simple microstructure optical fiber design based on an octagonal cladding structure is presented for simultaneously controlling dispersion and leakage properties. The finite difference method with anisotropic perfectly matched boundary layer is used to investigate the guiding properties. It is demonstrated that octagonal photonic crystal fibers with four rings can assume negative ultra-flattened dispersion of -19 + 0.23 ps/nm/km in the wavelength range of 1.275 μm to 1.68 μm, nearly zero ultra-flattened dispersion of 0 ± 0.40 ps/nm/km in a 1.38 to 1.64 μm, and low confinement losses less than 10-3 dB/km in the entire band of interest.
Abstract: The paper deals with a mathematical model for fluid dynamic flows on road networks which is based on conservation laws. This nonlinear framework is based on the conservation of cars. We focus on traffic circle, which is a finite number of roads that meet at some junctions. The traffic circle with junctions having either one incoming and two outgoing or two incoming and one outgoing roads. We describe the numerical schemes with the particular boundary conditions used to produce approximated solutions of the problem.
Abstract: An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.
Abstract: The disaster from functional gastrointestinal disorders has detrimental impact on the quality of life of the effected population and imposes a tremendous social and economic burden. There are, however, rare diagnostic methods for the functional gastrointestinal disorders. Our research group identified recently that the gastrointestinal tract well in the patients with the functional gastrointestinal disorders becomes more rigid than healthy people when palpating the abdominal regions overlaying the gastrointestinal tract. Objective of current study is, therefore, identify feasibility of a diagnostic system for the functional gastrointestinal disorders based on ultrasound technique, which can quantify the characteristics above. Two-dimensional finite difference (FD) models (one normal and two rigid model) were developed to analyze the reflective characteristic (displacement) on each soft-tissue layer responded after application of ultrasound signals. The FD analysis was then based on elastic ultrasound theory. Validation of the model was performed via comparison of the characteristic of the ultrasonic responses predicted by FD analysis with that determined from the actual specimens for the normal and rigid conditions. Based on the results from FD analysis, ultrasound system for diagnosis of the functional gastrointestinal disorders was developed and clinically tested via application of it to 40 human subjects with/without functional gastrointestinal disorders who were assigned to Normal and Patient Groups. The FD models were favorably validated. The results from FD analysis showed that the maximum displacement amplitude in the rigid models (0.12 and 0.16) at the interface between the fat and muscle layers was explicitly less than that in the normal model (0.29). The results from actual specimens showed that the maximum amplitude of the ultrasonic reflective signal in the rigid models (0.2±0.1Vp-p) at the interface between the fat and muscle layers was explicitly higher than that in the normal model (0.1±0.2 Vp-p). Clinical tests using our customized ultrasound system showed that the maximum amplitudes of the ultrasonic reflective signals near to the gastrointestinal tract well for the patient group (2.6±0.3 Vp-p) were generally higher than those in normal group (0.1±0.2 Vp-p). Here, maximum reflective signals was appeared at 20mm depth approximately from abdominal skin for all human subjects, corresponding to the location of the boundary layer close to gastrointestinal tract well. These findings suggest that our customized ultrasound system using the ultrasonic reflective signal may be helpful to the diagnosis of the functional gastrointestinal disorders.
Abstract: In this paper, an alternating implicit block method for
solving two dimensional scalar wave equation is presented. The
new method consist of two stages for each time step implemented
in alternating directions which are very simple in computation. To
increase the speed of computation, a group of adjacent points is
computed simultaneously. It is shown that the presented method
increase the maximum time step size and more accurate than the
conventional finite difference time domain (FDTD) method and other
existing method of natural ordering.
Abstract: Smoke discharging is a main reason of air pollution
problem from industrial plants. The obstacle of a building has an
affect with the air pollutant discharge. In this research, a mathematical
model of the smoke dispersion from two sources and one source with
a structural obstacle is considered. The governing equation of the
model is an isothermal mass transfer model in a viscous fluid. The
finite element method is used to approximate the solutions of the
model. The triangular linear elements have been used for discretising
the domain, and time integration has been carried out by semi-implicit
finite difference method. The simulations of smoke dispersion in
cases of one chimney and two chimneys are presented. The maximum
calculated smoke concentration of both cases are compared. It is then
used to make the decision for smoke discharging and air pollutant
control problems on industrial area.