Abstract: In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.
Abstract: This analysis investigates the distortion of flow
measurement and the increase of cavitation along orifice
flowmeter. The analysis using the numerical method (CFD)
validated the distortion of flow measurement through the inlet
velocity profile considering the convergence and grid
dependency. Realizable k-e model was selected and y+ was
about 50 in this numerical analysis. This analysis also estimated
the vulnerability of cavitation effect due to inlet velocity profile.
The investigation concludes that inclined inlet velocity profile
could vary the pressure which was measured at pressure tab
near pipe wall and it led to distort the pressure values ranged
from -3.8% to 5.3% near the orifice plate and to make the
increase of cavitation. The investigation recommends that the
fully developed inlet velocity flow is beneficial to accurate flow
measurement in orifice flowmeter.
Abstract: A new numerical method for solving the twodimensional,
steady, incompressible, viscous flow equations on a
Curvilinear staggered grid is presented in this paper. The proposed
methodology is finite difference based, but essentially takes
advantage of the best features of two well-established numerical
formulations, the finite difference and finite volume methods. Some
weaknesses of the finite difference approach are removed by
exploiting the strengths of the finite volume method. In particular,
the issue of velocity-pressure coupling is dealt with in the proposed
finite difference formulation by developing a pressure correction
equation in a manner similar to the SIMPLE approach commonly
used in finite volume formulations. However, since this is purely a
finite difference formulation, numerical approximation of fluxes is
not required. Results obtained from the present method are based on
the first-order upwind scheme for the convective terms, but the
methodology can easily be modified to accommodate higher order
differencing schemes.
Abstract: The development and extension of large cities induced
a need for shallow tunnel in soft ground of building areas. Estimation
of ground settlement caused by the tunnel excavation is important
engineering point. In this paper, prediction of surface subsidence
caused by tunneling in one section of seventh line of Tehran subway
is considered. On the basis of studied geotechnical conditions of the
region, tunnel with the length of 26.9km has been excavated applying
a mechanized method using an EPB-TBM with a diameter of 9.14m.
In this regard, settlement is estimated utilizing both analytical and
numerical finite element method. The numerical method shows that
the value of settlement in this section is 5cm. Besides, the analytical
consequences (Bobet and Loganathan-Polous) are 5.29 and 12.36cm,
respectively. According to results of this study, due tosaturation of
this section, there are good agreement between Bobet and numerical
methods. Therefore, tunneling processes in this section needs a
special consolidation measurement and support system before the
passage of tunnel boring machine.
Abstract: In the present study, the pressure drop and laminar convection heat transfer characteristics of nanofluids in microchannel heat sink with square duct are numerically investigated. The water based nanofluids created with Al2O3 and CuO particles in four different volume fractions of 0%, 0.5%, 1%, 1.5% and 2% are used to analyze their effects on heat transfer and the pressure drop. Under the laminar, steady-state flow conditions, the finite volume method is used to solve the governing equations of heat transfer. Mixture Model is considered to simulate the nanofluid flow. For verification of used numerical method, the results obtained from numerical calculations were compared with the results in literature for both pure water and the nanofluids in different volume fractions. The distributions of the particles in base fluid are assumed to be uniform. The results are evaluated in terms of Nusselt number, the pressure drop and heat transfer enhancement. Analysis shows that the nanofluids enhance heat transfer while the Reynolds number and the volume fractions are increasing. The best overall enhancement was obtained at φ=%2 and Re=100 for CuO-water nanofluid.
Abstract: The present paper develops and validates a numerical procedure for the calculation of turbulent combustive flow in converging and diverging ducts and throuh simulation of the heat transfer processes, the amount of production and spread of Nox pollutant has been measured. A marching integration solution procedure employing the TDMA is used to solve the discretized equations. The turbulence model is the Prandtl Mixing Length method. Modeling the combustion process is done by the use of Arrhenius and Eddy Dissipation method. Thermal mechanism has been utilized for modeling the process of forming the nitrogen oxides. Finite difference method and Genmix numerical code are used for numerical solution of equations. Our results indicate the important influence of the limiting diverging angle of diffuser on the coefficient of recovering of pressure. Moreover, due to the intense dependence of Nox pollutant to the maximum temperature in the domain with this feature, the Nox pollutant amount is also in maximum level.
Abstract: In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.
Abstract: In this paper, the computation of the electrical field distribution around AC high-voltage lines is demonstrated. The advantages and disadvantages of two different methods are described to evaluate the electrical field quantity. The first method is a seminumerical method using the laws of electrostatic techniques to simulate the two-dimensional electric field under the high-voltage overhead line. The second method which will be discussed is the finite element method (FEM) using specific boundary conditions to compute the two- dimensional electric field distributions in an efficient way.
Abstract: In this paper, we explore the applicability of the Sinc-
Collocation method to a three-dimensional (3D) oceanography model.
The model describes a wind-driven current with depth-dependent
eddy viscosity in the complex-velocity system. In general, the
Sinc-based methods excel over other traditional numerical methods
due to their exponentially decaying errors, rapid convergence and
handling problems in the presence of singularities in end-points.
Together with these advantages, the Sinc-Collocation approach that
we utilize exploits first derivative interpolation, whose integration
is much less sensitive to numerical errors. We bring up several
model problems to prove the accuracy, stability, and computational
efficiency of the method. The approximate solutions determined by
the Sinc-Collocation technique are compared to exact solutions and
those obtained by the Sinc-Galerkin approach in earlier studies. Our
findings indicate that the Sinc-Collocation method outperforms other
Sinc-based methods in past studies.
Abstract: Recently, bianisotropic media again received
increasing importance in electromagnetic theory because of advances
in material science which enable the manufacturing of complex
bianisotropic materials. By using Maxwell's equations and
corresponding boundary conditions, the electromagnetic field
distribution in bianisotropic solenoid coils is determined and the
influence of the bianisotropic behaviour of coil to the impedance and
Q-factor is considered. Bianisotropic media are the largest class of
linear media which is able to describe the macroscopic material
properties of artificial dielectrics, artificial magnetics, artificial chiral
materials, left-handed materials, metamaterials, and other composite
materials. Several special cases of coils, filled with complex
substance, have been analyzed. Results obtained by using the
analytical approach are compared with values calculated by
numerical methods, especially by our new hybrid EEM/BEM method
and FEM.
Abstract: Resistance spot welding process comprises of electric,
thermal and mechanical phenomenon, which makes this process
complex and highly non-linear and thus, it becomes difficult to model
it. In order to obtain good weld nugget during spot welding, hit and
trial welds are usually done which is very costly. Therefore the
numerical simulation research has been conducted to understand the
whole process. In this paper three different cases were analyzed by
varying the tip contact area and it was observed that, with the
variation of tip contact area the nugget formation at the faying
surface is affected. The tip contact area of the welding electrode
becomes large with long welding cycles. Therefore in order to
maintain consistency of nugget formation during the welding process,
the current compensation in control feedback is required. If the
contact area of the welding electrode tip is reduced, a large amount of
current flows through the faying surface, as a result of which
sputtering occurs.
Abstract: In this paper, the local grid refinement is focused by
using a nested grid technique. The Cartesian grid numerical method is
developed for simulating unsteady, viscous, incompressible flows
with complex immersed boundaries. A finite volume method is used in
conjunction with a two-step fractional-step procedure. The key aspects
that need to be considered in developing such a nested grid solver are
imposition of interface conditions on the inter-block and accurate
discretization of the governing equation in cells that are with the
inter-block as a control surface. A new interpolation procedure is
presented which allows systematic development of a spatial
discretization scheme that preserves the spatial accuracy of the
underlying solver. The present nested grid method has been tested by
two numerical examples to examine its performance in the two
dimensional problems. The numerical examples include flow past a
circular cylinder symmetrically installed in a Channel and flow past
two circular cylinders with different diameters. From the numerical
experiments, the ability of the solver to simulate flows with
complicated immersed boundaries is demonstrated and the nested grid
approach can efficiently speed up the numerical solutions.
Abstract: The objective of this paper is to study the analysis and testing for determining the torsional stiffness of the student formula-s space frame. From past study, the space frame for Chulalongkorn University Student Formula team used in 2011 TSAE Auto Challenge Student Formula in Thailand was designed by considering required mass and torsional stiffness based on the numerical method and experimental method. The numerical result was compared with the experimental results to verify the torsional stiffness of the space frame. It can be seen from the large error of torsional stiffness of 2011 frame that the experimental result can not verify by the numerical analysis due to the different between the numerical model and experimental setting. In this paper, the numerical analysis and experiment of the same 2011 frame model is performed by improving the model setting. The improvement of both numerical analysis and experiment are discussed to confirm that the models from both methods are same. After the frame was analyzed and tested, the results are compared to verify the torsional stiffness of the frame. It can be concluded that the improved analysis and experiments can used to verify the torsional stiffness of the space frame.
Abstract: In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by = 0. Ôêé Ôêé + Ôêé Ôêé x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised schemes designed by Tam and Webb, Lockard et al., Zingg et al., Zhuang and Chen, Bogey and Bailly. Thus, these seven different spatial derivatives have been coupled with the optimised time derivative to obtain seven different finite-difference schemes to approximate the linear advection equation. We have analysed the variation of the modified wavenumber and group velocity, both with respect to the exact wavenumber for each spatial derivative. The problems considered are the 1-D propagation of a Boxcar function, propagation of an initial disturbance consisting of a sine and Gaussian function and the propagation of a Gaussian profile. It is known that the choice of the cfl number affects the quality of results in terms of dissipation and dispersion characteristics. Based on the numerical experiments solved and numerical methods used to approximate the linear advection equation, it is observed in this work, that the quality of results is dependent on the choice of the cfl number, even for optimised numerical methods. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Also, the quantity, Exponential Error for Low Dispersion and Low Dissipation, eeldld has been computed from the numerical results. Moreover, based on this work, it has been found that when the quantity, eeldld can be used as a measure of the total error. In particular, the total error is a minimum when the eeldld is a minimum.
Abstract: Adhesively bonded joints are preferred over the
conventional methods of joining such as riveting, welding, bolting
and soldering. Some of the main advantages of adhesive joints
compared to conventional joints are the ability to join dissimilar
materials and damage-sensitive materials, better stress distribution,
weight reduction, fabrication of complicated shapes, excellent
thermal and insulation properties, vibration response and enhanced
damping control, smoother aerodynamic surfaces and an
improvement in corrosion and fatigue resistance. This paper presents
the behavior of adhesively bonded joints subjected to combined
thermal loadings, using the numerical methods. The joint
configuration considers aluminum as central adherend with six
different outer adherends including aluminum, steel, titanium, boronepoxy,
unidirectional graphite-epoxy and cross-ply graphite-epoxy
and epoxy-based adhesives. Free expansion of the joint in x
direction was permitted and stresses in adhesive layer and interfaces
calculated for different adherends.
Abstract: Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.
Abstract: A general purpose viscous flow solver Ansys CFX
was used to solve the unsteady three-dimensional (3D) Reynolds
Averaged Navier-Stokes Equation (RANSE) for simulating a 3D
numerical viscous wave tank. A flap-type wave generator was
incorporated in the computational domain to generate the desired
incident waves. Authors have made effort to study the physical
behaviors of Flap type wave maker with governing parameters.
Dependency of the water fill depth, Time period of oscillations and
amplitude of oscillations of flap were studied. Effort has been made
to establish relations between parameters. A validation study was
also carried out against CFD methodology with wave maker theory.
It has been observed that CFD results are in good agreement with
theoretical results. Beaches of different slopes were introduced to
damp the wave, so that it should not cause any reflection from
boundary. As a conclusion this methodology can simulate the
experimental wave-maker for regular wave generation for different
wave length and amplitudes.
Abstract: In contrast to existing of calculation of temperature field of a profile part a blade with convective cooling which are not taking into account multi connective in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM AND FDM) numerical methods from the point of view of a realization on the PC. The theoretical substantiation of these methods is proved by the appropriate theorems.
Abstract: This paper examines many mathematical methods for
molding the hourly price forward curve (HPFC); the model will be
constructed by numerous regression methods, like polynomial
regression, radial basic function neural networks & a furrier series.
Examination the models goodness of fit will be done by means of
statistical & graphical tools. The criteria for choosing the model will
depend on minimize the Root Mean Squared Error (RMSE), using the
correlation analysis approach for the regression analysis the optimal
model will be distinct, which are robust against model
misspecification. Learning & supervision technique employed to
determine the form of the optimal parameters corresponding to each
measure of overall loss. By using all the numerical methods that
mentioned previously; the explicit expressions for the optimal model
derived and the optimal designs will be implemented.
Abstract: In this article an evolutionary technique has been used
for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for
the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been
successfully applied to solve the different forms of Riccati
differential equations. The strength of proposed method has in its
equal applicability for the integer order case, as well as, fractional
order case. Comparison of the method has been made with standard
numerical techniques as well as the analytic solutions. It is found
that the designed method can provide the solution to the equation
with better accuracy than its counterpart deterministic approaches.
Another advantage of the given approach is to provide results on
entire finite continuous domain unlike other numerical methods
which provide solutions only on discrete grid of points.