Abstract: The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.
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: The RK5GL3 method is a numerical method for solving
initial value problems in ordinary differential equations, and is
based on a combination of a fifth-order Runge-Kutta method and
3-point Gauss-Legendre quadrature. In this paper we describe an
effective local error control algorithm for RK5GL3, which uses local
extrapolation with an eighth-order Runge-Kutta method in tandem
with RK5GL3, and a Hermite interpolating polynomial for solution
estimation at the Gauss-Legendre quadrature nodes.
Abstract: The paper provides a numerical investigation of the
entropy generation analysis due to natural convection in an inclined
square porous cavity. The coupled equations of mass, momentum,
energy and species conservation are solved using the Control Volume
Finite-Element Method. Effect of medium permeability and
inclination angle on entropy generation is analysed. It was found that
according to the Darcy number and the porous thermal Raleigh
number values, the entropy generation could be mainly due to heat
transfer or to fluid friction irreversibility and that entropy generation
reaches extremum values for specific inclination angles.
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: 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: In this study, aeroelastic response and performance
analyses have been conducted for a 5MW-Class composite wind
turbine blade model. Advanced coupled numerical method based on
computational fluid dynamics (CFD) and computational flexible
multi-body dynamics (CFMBD) has been developed in order to
investigate aeroelastic responses and performance characteristics of
the rotating composite blade. Reynolds-Averaged Navier-Stokes
(RANS) equations with k-ω SST turbulence model were solved for
unsteady flow problems on the rotating turbine blade model. Also,
structural analyses considering rotating effect have been conducted
using the general nonlinear finite element method. A fully implicit
time marching scheme based on the Newmark direct integration
method is applied to solve the coupled aeroelastic governing equations
of the 3D turbine blade for fluid-structure interaction (FSI) problems.
Detailed dynamic responses and instantaneous velocity contour on the
blade surfaces which considering flow-separation effects were
presented to show the multi-physical phenomenon of the huge rotating
wind- turbine blade model.
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: A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.
Abstract: A numerical method is developed for simulating
the motion of particles with arbitrary shapes in an effectively
infinite or bounded viscous flow. The particle translational and
angular motions are numerically investigated using a fluid-structure
interaction (FSI) method based on the Arbitrary-Lagrangian-Eulerian
(ALE) approach and the dynamic mesh method (smoothing and
remeshing) in FLUENT ( ANSYS Inc., USA). Also, the effects of
arbitrary shapes on the dynamics are studied using the FSI method
which could be applied to the motions and deformations of a single
blood cell and multiple blood cells, and the primary thrombogenesis
caused by platelet aggregation. It is expected that, combined with a
sophisticated large-scale computational technique, the simulation
method will be useful for understanding the overall properties of blood
flow from blood cellular level (microscopic) to the resulting
rheological properties of blood as a mass (macroscopic).
Abstract: In this paper, a numerical solution based on nonpolynomial
cubic spline functions is used for finding the solution of
boundary value problems which arise from the problems of calculus
of variations. This approximation reduce the problems to an explicit
system of algebraic equations. Some numerical examples are also
given to illustrate the accuracy and applicability of the presented
method.
Abstract: We consider a network of two M/M/1 parallel queues having the same poisonnian arrival stream with rate λ. Upon his arrival to the system a customer heads to the shortest queue and stays until being served. If the two queues have the same length, an arriving customer chooses one of the two queues with the same probability. Each duration of service in the two queues is an exponential random variable with rate μ and no jockeying is permitted between the two queues. A new numerical method, based on linear programming and convex optimization, is performed for the computation of the steady state solution of the system.
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: Supplier selection is a multi criteria decision-making process that comprises tangible and intangible factors. The majority of previous supplier selection techniques do not consider strategic perspective. Besides, uncertainty is one of the most important obstacles in supplier selection. For the first, time in this paper, the idea of the algorithm " Knapsack " is used to select suppliers Moreover, an attempt has to be made to take the advantage of a simple numerical method for solving model .This is an innovation to resolve any ambiguity in choosing suppliers. This model has been tried in the suppliers selected in a competitive environment and according to all desired standards of quality and quantity to show the efficiency of the model, an industry sample has been uses.
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.
Abstract: Modeling transfer phenomena in several chemical
engineering operations leads to the resolution of partial differential
equations systems. According to the complexity of the operations
mechanisms, the equations present a nonlinear form and analytical
solution became difficult, we have then to use numerical methods
which are based on approximations in order to transform a
differential system to an algebraic one.Finite element method is one
of numerical methods which can be used to obtain an accurate
solution in many complex cases of chemical engineering.The packed
columns find a large application like contactor for liquid-liquid
systems such solvent extraction. In the literature, the modeling of this
type of equipment received less attention in comparison with the
plate columns.A mathematical bidimensionnal model with radial and
axial dispersion, simulating packed tower extraction behavior was
developed and a partial differential equation was solved using the
finite element method by adopting the Galerkine model. We
developed a Mathcad program, which can be used for a similar
equations and concentration profiles are obtained along the column.
The influence of radial dispersion was prooved and it can-t be
neglected, the results were compared with experimental concentration
at the top of the column in the extraction system:
acetone/toluene/water.
Abstract: As a part of the development of a numerical method of
close capture exhausts systems for machining devices, a test rig
recreating a situation similar to a grinding operation, but in a
perfectly controlled environment, is used. The properties of the
obtained spray of solid particles are initially characterized using
particle tracking velocimetry (PTV), in order to obtain input and
validation parameters for numerical simulations. The dispersion of a
tracer gas (SF6) emitted simultaneously with the particle jet is then
studied experimentally, as the dispersion of such a gas is
representative of that of finer particles, whose aerodynamic response
time is negligible. Finally, complete modeling of the test rig is
achieved to allow comparison with experimental results and thus to
progress towards validation of the models used to describe a twophase
flow generated by machining operation.