Abstract: In this paper Lattice Boltzmann simulation of
turbulent natural convection with large-eddy simulations (LES) in a
square cavity which is filled by water has been investigated. The
present results are validated by finds of other investigations which
have been done with different numerical methods. Calculations were
performed for high Rayleigh numbers of Ra=108 and 109. The results
confirm that this method is in acceptable agreement with other
verifications of such a flow. In this investigation is tried to present
Large-eddy turbulence flow model by Lattice Boltzmann Method
(LBM) with a clear and simple statement. Effects of increase in
Rayleigh number are displayed on streamlines, isotherm counters and
average Nusselt number. Result shows that the average Nusselt
number enhances with growth of the Rayleigh numbers.
Abstract: Taking into account that many problems of natural
sciences and engineering are reduced to solving initial-value problem
for ordinary differential equations, beginning from Newton, the
scientists investigate approximate solution of ordinary differential
equations. There are papers of different authors devoted to the
solution of initial value problem for ODE. The Euler-s known
method that was developed under the guidance of the famous
scientists Adams, Runge and Kutta is the most popular one among
these methods.
Recently the scientists began to construct the methods preserving
some properties of Adams and Runge-Kutta methods and called them
hybrid methods. The constructions of such methods are investigated
from the middle of the XX century. Here we investigate one
generalization of multistep and hybrid methods and on their base we
construct specific methods of accuracy order p = 5 and p = 6 for
k = 1 ( k is the order of the difference method).
Abstract: In this paper the supersonic ejectors are
experimentally and analytically studied. Ejector is a device that
uses the energy of a fluid to move another fluid. This device works
like a vacuum pump without usage of piston, rotor or any other
moving component. An ejector contains an active nozzle, a passive
nozzle, a mixing chamber and a diffuser. Since the fluid viscosity
is large, and the flow is turbulent and three dimensional in the
mixing chamber, the numerical methods consume long time and
high cost to analyze the flow in ejectors. Therefore this paper
presents a simple analytical method that is based on the precise
governing equations in fluid mechanics. According to achieved
analytical relations, a computer code has been prepared to analyze
the flow in different components of the ejector. An experiment has
been performed in supersonic regime 1.5
Abstract: In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasistationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine first stage nozzle blade.
Abstract: Tubular process equipment is often damaged in
industrial processes. The damage occurs both on devices working at
high temperatures and also on less exposed devices. In case of sudden
damage of key equipment a shutdown of the whole production unit
and resulting significant economic losses are imminent. This paper
presents a solution of several types of tubular process equipment. The
causes of damage and suggestions of correction actions are discussed
in all cases. Very important part is the analysis of operational
conditions, determination of unfavourable working states decreasing
lifetime of devices and suggestions of correction actions. Lately very
popular numerical methods are used for analysis of the equipment.
Abstract: The aim of this paper is to investigate the
performance of the developed two point block method designed for
two processors for solving directly non stiff large systems of higher
order ordinary differential equations (ODEs). The method calculates
the numerical solution at two points simultaneously and produces
two new equally spaced solution values within a block and it is
possible to assign the computational tasks at each time step to a
single processor. The algorithm of the method was developed in C
language and the parallel computation was done on a parallel shared
memory environment. Numerical results are given to compare the
efficiency of the developed method to the sequential timing. For
large problems, the parallel implementation produced 1.95 speed-up
and 98% efficiency for the two processors.
Abstract: According to the new developments in the field of information and communication technologies, the necessity arises for active use of these new technologies in education. It is clear that the integration of technology in education system will be different for primary-higher education or traditional- distance education. In this study, the subject of the integration of technology for distance education was discussed. The subject was taken from the viewpoint of students. With using the information of student feedback about education program in which new technological medias are used, how can survey variables can be separated into the factors as positive, negative and supporter and how can be redesigned education strategy of the higher education associations with the examining the variables of each determinated factor is explained. The paper concludes with the recommendations about the necessitity of working as a group of different area experts and using of numerical methods in establishing of education strategy to be successful.
Abstract: An evolutionary computing technique for solving initial value problems in Ordinary Differential Equations is proposed in this paper. Neural network is used as a universal approximator while the adaptive parameters of neural networks are optimized by genetic algorithm. The solution is achieved on the continuous grid of time instead of discrete as in other numerical techniques. The comparison is carried out with classical numerical techniques and the solution is found with a uniform accuracy of MSE ≈ 10-9 .
Abstract: The dynamics of a predator-prey model with continuous
threshold policy harvesting functions on the prey is studied. Theoretical
and numerical methods are used to investigate boundedness
of solutions, existence of bionomic equilibria, and the stability properties
of coexistence equilibrium points and periodic orbits. Several
bifurcations as well as some heteroclinic orbits are computed.
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: Avalanche release of snow has been modeled in the present studies. Snow is assumed to be represented by semi-solid and the governing equations have been studied from the concept of continuum approach. The dynamical equations have been solved for two different zones [starting zone and track zone] by using appropriate initial and boundary conditions. Effect of density (ρ), Eddy viscosity (η), Slope angle (θ), Slab depth (R) on the flow parameters have been observed in the present studies. Numerical methods have been employed for computing the non linear differential equations. One of the most interesting and fundamental innovation in the present studies is getting initial condition for the computation of velocity by numerical approach. This information of the velocity has obtained through the concept of fracture mechanics applicable to snow. The results on the flow parameters have found to be in qualitative agreement with the published results.
Abstract: In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and cvazistationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine 1st stage nozzle blade
Abstract: Implicit equations play a crucial role in Engineering.
Based on this importance, several techniques have been applied to
solve this particular class of equations. When it comes to practical
applications, in general, iterative procedures are taken into account.
On the other hand, with the improvement of computers, other
numerical methods have been developed to provide a more
straightforward methodology of solution. Analytical exact approaches
seem to have been continuously neglected due to the difficulty
inherent in their application; notwithstanding, they are indispensable
to validate numerical routines. Lagrange-s Inversion Theorem is a
simple mathematical tool which has proved to be widely applicable to
engineering problems. In short, it provides the solution to implicit
equations by means of an infinite series. To show the validity of this
method, the tree-parameter infiltration equation is, for the first time,
analytically and exactly solved. After manipulating these series,
closed-form solutions are presented as H-functions.
Abstract: The two-phase flow field and the motion of the free
surface in an oscillating channel are simulated numerically to assess
the methodology for simulating nuclear reacotr thermal hydraulics
under seismic conditions. Two numerical methods are compared: one
is to model the oscillating channel directly using the moving grid of
the Arbitrary Lagrangian-Eulerian method, and the other is to simulate
the effect of channel motion using the oscillating acceleration acting
on the fluid in the stationary channel. The two-phase flow field in the
oscillating channel is simulated using the level set method in both
cases. The calculated results using the oscillating acceleration are
found to coinside with those using the moving grid, and the theoretical
back ground and the limitation of oscillating acceleration are discussed.
It is shown that the change in the interfacial area between liquid and
gas phases under seismic conditions is important for nuclear reactor
thermal hydraulics.
Abstract: The flow field and the motion of the free surface in an
oscillating container are simulated numerically to assess the numerical
approach for studying two-phase flows under oscillating conditions.
Two numerical methods are compared: one is to model the oscillating
container directly using the moving grid of the ALE method, and the
other is to simulate the effect of container motion using the oscillating
body force acting on the fluid in the stationary container. The
two-phase flow field in the container is simulated using the level set
method in both cases. It is found that the calculated results by the body
force method coinsides with those by the moving grid method and the
sloshing behavior is predicted well by both the methods. Theoretical
back ground and limitation of the body force method are discussed,
and the effects of oscillation amplitude and frequency are shown.
Abstract: In this paper we present discretization and decomposition methods for a multi-component transport model of a chemical vapor deposition (CVD) process. CVD processes are used to manufacture deposition layers or bulk materials. In our transport model we simulate the deposition of thin layers. The microscopic model is based on the heavy particles, which are derived by approximately solving a linearized multicomponent Boltzmann equation. For the drift-process of the particles we propose diffusionreaction equations as well as for the effects of heat conduction. We concentrate on solving the diffusion-reaction equation with analytical and numerical methods. For the chemical processes, modelled with reaction equations, we propose decomposition methods and decouple the multi-component models to simpler systems of differential equations. In the numerical experiments we present the computational results of our proposed models.
Abstract: In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.
Abstract: In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.
Abstract: This paper proposes a set of quasi-static mathematical
model of magnetic fields caused by high voltage conductors of
distribution transformer by using a set of second-order partial
differential equation. The modification for complex magnetic field
analysis and time-harmonic simulation are also utilized. In this
research, transformers were study in both balanced and unbalanced
loading conditions. Computer-based simulation utilizing the threedimensional
finite element method (3-D FEM) is exploited as a tool
for visualizing magnetic fields distribution volume a distribution
transformer. Finite Element Method (FEM) is one among popular
numerical methods that is able to handle problem complexity in
various forms. At present, the FEM has been widely applied in most
engineering fields. Even for problems of magnetic field distribution,
the FEM is able to estimate solutions of Maxwell-s equations
governing the power transmission systems. The computer simulation
based on the use of the FEM has been developed in MATLAB
programming environment.
Abstract: Different numerical methods are employed and developed for simulating interfacial flows. A large range of applications belong to this group, e.g. two-phase flows of air bubbles in water or water drops in air. In such problems surface tension effects often play a dominant role. In this paper, various models of surface tension force for interfacial flows, the CSF, CSS, PCIL and SGIP models have been applied to simulate the motion of small air bubbles in water and the results were compared and reviewed. It has been pointed out that by using SGIP or PCIL models, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.