Abstract: In this paper, a backward semi-Lagrangian scheme
combined with the second-order backward difference formula
is designed to calculate the numerical solutions of nonlinear
advection-diffusion equations. The primary aims of this paper are
to remove any iteration process and to get an efficient algorithm
with the convergence order of accuracy 2 in time. In order to achieve
these objects, we use the second-order central finite difference and the
B-spline approximations of degree 2 and 3 in order to approximate
the diffusion term and the spatial discretization, respectively. For the
temporal discretization, the second order backward difference formula
is applied. To calculate the numerical solution of the starting point
of the characteristic curves, we use the error correction methodology
developed by the authors recently. The proposed algorithm turns out
to be completely iteration free, which resolves the main weakness
of the conventional backward semi-Lagrangian method. Also, the
adaptability of the proposed method is indicated by numerical
simulations for Burgers’ equations. Throughout these numerical
simulations, it is shown that the numerical results is in good
agreement with the analytic solution and the present scheme offer
better accuracy in comparison with other existing numerical schemes.
Abstract: Accurate dynamic modeling and analysis of flexible link manipulator (FLM) with non linear dynamics is very difficult due to distributed link flexibility and few studies have been conducted based on assumed modes method (AMM) and finite element models. In this paper a nonlinear dynamic model with first two elastic modes is derived using combined Euler/Lagrange and AMM approaches. Significant dynamics associated with the system such as hub inertia, payload, structural damping, friction at joints, combined link and joint flexibility are incorporated to obtain the complete and accurate dynamic model. The response of the FLM to the applied bang-bang torque input is compared against the models derived from LS-DYNA finite element discretization approach and linear finite element models. Dynamic analysis is conducted using LS-DYNA finite element model which uses the explicit time integration scheme to simulate the system. Parametric study is conducted to show the impact payload mass. A numerical result shows that the LS-DYNA model gives the smooth hub-angle profile.
Abstract: The objective in this work is to generate and discuss the stability results of fully-immersed end-milling process with parameters; tool mass m=0.0431kg,tool natural frequency ωn = 5700 rads^-1, damping factor ξ=0.002 and workpiece cutting coefficient C=3.5x10^7 Nm^-7/4. Different no of teeth is considered for the end-milling. Both 1-DOF and 2-DOF chatter models of the system are generated on the basis of non-linear force law. Chatter stability analysis is carried out using a modified form (generalized for both 1-DOF and 2-DOF models) of recently developed method called Full-discretization. The full-immersion three tooth end-milling together with higher toothed end-milling processes has secondary Hopf bifurcation lobes (SHBL’s) that exhibit one turning (minimum) point each. Each of such SHBL is demarcated by its minimum point into two portions; (i) the Lower Spindle Speed Portion (LSSP) in which bifurcations occur in the right half portion of the unit circle centred at the origin of the complex plane and (ii) the Higher Spindle Speed Portion (HSSP) in which bifurcations occur in the left half portion of the unit circle. Comments are made regarding why bifurcation lobes should generally get bigger and more visible with increase in spindle speed and why flip bifurcation lobes (FBL’s) could be invisible in the low-speed stability chart but visible in the high-speed stability chart of the fully-immersed three-tooth miller.
Abstract: We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.
Abstract: Sometime it is difficult to determine the exact reliability for complex systems in analytical procedures. Approximate solution of this problem can be provided through discretization of random variables. In this paper we describe the usefulness of discretization of a random variable using the reversed hazard rate function of its continuous version. Discretization of the exponential distribution has been demonstrated. Applications of this approach have also been cited. Numerical calculations indicate that the proposed approach gives very good approximation of reliability of complex systems under stress-strength set-up. The performance of the proposed approach is better than the existing discrete concentration method of discretization. This approach is conceptually simple, handles analytic intractability and reduces computational time. The approach can be applied in manufacturing industries for producing high-reliable items.
Abstract: A method for simulating flow around the solid bodies has been presented using hybrid meshfree and mesh-based schemes. The presented scheme optimizes the computational efficiency by combining the advantages of both meshfree and mesh-based methods. In this approach, a cloud of meshfree nodes has been used in the domain around the solid body. These meshfree nodes have the ability to efficiently adapt to complex geometrical shapes. In the rest of the domain, conventional Cartesian grid has been used beyond the meshfree cloud. Complex geometrical shapes can therefore be dealt efficiently by using meshfree nodal cloud and computational efficiency is maintained through the use of conventional mesh-based scheme on Cartesian grid in the larger part of the domain. Spatial discretization of meshfree nodes has been achieved through local radial basis functions in finite difference mode (RBF-FD). Conventional finite difference scheme has been used in the Cartesian ‘meshed’ domain. Accuracy tests of the hybrid scheme have been conducted to establish the order of accuracy. Numerical tests have been performed by simulating two dimensional steady and unsteady incompressible flows around cylindrical object. Steady flow cases have been run at Reynolds numbers of 10, 20 and 40 and unsteady flow problems have been studied at Reynolds numbers of 100 and 200. Flow Parameters including lift, drag, vortex shedding, and vorticity contours are calculated. Numerical results have been found to be in good agreement with computational and experimental results available in the literature.
Abstract: The exponential increase in the volume of medical image database has imposed new challenges to clinical routine in maintaining patient history, diagnosis, treatment and monitoring. With the advent of data mining and machine learning techniques it is possible to automate and/or assist physicians in clinical diagnosis. In this research a medical image classification framework using data mining techniques is proposed. It involves feature extraction, feature selection, feature discretization and classification. In the classification phase, the performance of the traditional kNN k nearest neighbor classifier is improved using a feature weighting scheme and a distance weighted voting instead of simple majority voting. Feature weights are calculated using the interestingness measures used in association rule mining. Experiments on the retinal fundus images show that the proposed framework improves the classification accuracy of traditional kNN from 78.57 % to 92.85 %.
Abstract: This work presents a numerical simulation of the interaction of an incident shock wave propagates from the left to the right with a cone placed in a tube at shock. The Mathematical model is based on a non stationary, viscous and axisymmetric flow. The Discretization of the Navier-stokes equations is carried out by the finite volume method in the integral form along with the Flux Vector Splitting method of Van Leer. Here, adequate combination of time stepping parameter, CFL coefficient and mesh size level is selected to ensure numerical convergence. The numerical simulation considers a shock tube filled with air. The incident shock wave propagates to the right with a determined Mach number and crosses the cone by leaving behind it a stationary detached shock wave in front of the nose cone. This type of interaction is observed according to the time of flow.
Abstract: This paper deals with a high-order accurate Runge
Kutta Discontinuous Galerkin (RKDG) method for the numerical
solution of the wave equation, which is one of the simple case of a
linear hyperbolic partial differential equation. Nodal DG method is
used for a finite element space discretization in 'x' by discontinuous
approximations. This method combines mainly two key ideas which
are based on the finite volume and finite element methods. The
physics of wave propagation being accounted for by means of
Riemann problems and accuracy is obtained by means of high-order
polynomial approximations within the elements. High order accurate
Low Storage Explicit Runge Kutta (LSERK) method is used for
temporal discretization in 't' that allows the method to be nonlinearly
stable regardless of its accuracy. The resulting RKDG
methods are stable and high-order accurate. The L1 ,L2 and L∞ error
norm analysis shows that the scheme is highly accurate and effective.
Hence, the method is well suited to achieve high order accurate
solution for the scalar wave equation and other hyperbolic equations.
Abstract: Discretization of spatial derivatives is an important
issue in meshfree methods especially when the derivative terms
contain non-linear coefficients. In this paper, various methods used
for discretization of second-order spatial derivatives are investigated
in the context of Smoothed Particle Hydrodynamics. Three popular
forms (i.e. "double summation", "second-order kernel derivation",
and "difference scheme") are studied using one-dimensional unsteady
heat conduction equation. To assess these schemes, transient response
to a step function initial condition is considered. Due to parabolic
nature of the heat equation, one can expect smooth and monotone
solutions. It is shown, however in this paper, that regardless of
the type of kernel function used and the size of smoothing radius,
the double summation discretization form leads to non-physical
oscillations which persist in the solution. Also, results show that when
a second-order kernel derivative is used, a high-order kernel function
shall be employed in such a way that the distance of inflection
point from origin in the kernel function be less than the nearest
particle distance. Otherwise, solutions may exhibit oscillations near
discontinuities unlike the "difference scheme" which unconditionally
produces monotone results.
Abstract: Fingerprint based identification system; one of a well
known biometric system in the area of pattern recognition and has
always been under study through its important role in forensic
science that could help government criminal justice community. In
this paper, we proposed an identification framework of individuals by
means of fingerprint. Different from the most conventional
fingerprint identification frameworks the extracted Geometrical
element features (GEFs) will go through a Discretization process.
The intention of Discretization in this study is to attain individual
unique features that could reflect the individual varianceness in order
to discriminate one person from another. Previously, Discretization
has been shown a particularly efficient identification on English
handwriting with accuracy of 99.9% and on discrimination of twins-
handwriting with accuracy of 98%. Due to its high discriminative
power, this method is adopted into this framework as an independent
based method to seek for the accuracy of fingerprint identification.
Finally the experimental result shows that the accuracy rate of
identification of the proposed system using Discretization is 100%
for FVC2000, 93% for FVC2002 and 89.7% for FVC2004 which is
much better than the conventional or the existing fingerprint
identification system (72% for FVC2000, 26% for FVC2002 and
32.8% for FVC2004). The result indicates that Discretization
approach manages to boost up the classification effectively, and
therefore prove to be suitable for other biometric features besides
handwriting and fingerprint.
Abstract: In this paper, we investigated vector control of an induction machine taking into account discretization problems of the command. In the purpose to show how to include in a discrete model of this current control and with rotor time constant update. The results of simulation obtained are very satisfaisant. That was possible thanks to the good choice of the values of the parameters of the regulators used which shows, the founded good of the method used, for the choice of the parameters of the discrete regulators. The simulation results are presented at the end of this paper.
Abstract: Biclustering is a very useful data mining technique for
identifying patterns where different genes are co-related based on a
subset of conditions in gene expression analysis. Association rules
mining is an efficient approach to achieve biclustering as in
BIMODULE algorithm but it is sensitive to the value given to its
input parameters and the discretization procedure used in the
preprocessing step, also when noise is present, classical association
rules miners discover multiple small fragments of the true bicluster,
but miss the true bicluster itself. This paper formally presents a
generalized noise tolerant bicluster model, termed as μBicluster. An
iterative algorithm termed as BIDENS based on the proposed model
is introduced that can discover a set of k possibly overlapping
biclusters simultaneously. Our model uses a more flexible method to
partition the dimensions to preserve meaningful and significant
biclusters. The proposed algorithm allows discovering biclusters that
hard to be discovered by BIMODULE. Experimental study on yeast,
human gene expression data and several artificial datasets shows that
our algorithm offers substantial improvements over several
previously proposed biclustering algorithms.
Abstract: Flow through micro and mini channels requires relatively
high driving pressure due to the large fluid pressure drop
through these channels. Consequently the forces acting on the walls of
the channel due to the fluid pressure are also large. Due to these forces
there are displacement fields set up in the solid substrate containing
the channels. If the movement of the substrate is constrained at some
points, then stress fields are established in the substrate. On the other
hand, if the deformation of the channel shape is sufficiently large
then its effect on the fluid flow is important to be calculated. Such
coupled fluid-solid systems form a class of problems known as fluidstructure
interactions. In the present work a co-located finite volume
discretization procedure on unstructured meshes is described for
solving fluid-structure interaction type of problems. A linear elastic
solid is assumed for which the effect of the channel deformation
on the flow is neglected. Thus the governing equations for the
fluid and the solid are decoupled and are solved separately. The
procedure is validated by solving two benchmark problems, one from
fluid mechanics and another from solid mechanics. A fluid-structure
interaction problem of flow through a U-shaped channel embedded
in a plate is solved.
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: This paper presents a study of laminar to turbulent transition on a profile specifically designed for wind turbine blades, the DU91-W2-250, which belongs to a class of wind turbine dedicated airfoils, developed by Delft University of Technology. A comparison between the experimental behavior of the airfoil studied at Delft wind tunnel and the numerical predictions of the commercial CFD solver ANSYS FLUENT® has been performed. The prediction capabilities of the Spalart-Allmaras turbulence model and of the γ-θ Transitional model have been tested. A sensitivity analysis of the numerical results to the spatial domain discretization has also been performed using four different computational grids, which have been created using the mesher GAMBIT®. The comparison between experimental measurements and CFD results have allowed to determine the importance of the numerical prediction of the laminar to turbulent transition, in order not to overestimate airfoil friction drag due to a fully turbulent-regime flow computation.
Abstract: A semi-analytic boundary discretization method, the Method of Auxiliary Sources (MAS) is used to analyze Optical Antennas consisting of metallic parts. In addition to standard dipoletype antennas, consisting of two pieces of metal, a new structure consisting of a single metal piece with a tiny groove in the center is analyzed. It is demonstrated that difficult numerical problems are caused because optical antennas exhibit strong material dispersion, loss, and plasmon-polariton effects that require a very accurate numerical simulation. This structure takes advantage of the Channel Plasmon-Polariton (CPP) effect and exhibits a strong enhancement of the electric field in the groove. Also primitive 3D antenna model with spherical nano particles is analyzed.
Abstract: The purpose of this study is to derive optimal shapes of
a body located in viscous flows by the finite element method using the
acoustic velocity and the four-step explicit scheme. The formulation
is based on an optimal control theory in which a performance function
of the fluid force is introduced. The performance function should be
minimized satisfying the state equation. This problem can be transformed
into the minimization problem without constraint conditions
by using the adjoint equation with adjoint variables corresponding to
the state equation. The performance function is defined by the drag
and lift forces acting on the body. The weighted gradient method
is applied as a minimization technique, the Galerkin finite element
method is used as a spatial discretization and the four-step explicit
scheme is used as a temporal discretization to solve the state equation
and the adjoint equation. As the interpolation, the orthogonal basis
bubble function for velocity and the linear function for pressure
are employed. In case that the orthogonal basis bubble function is
used, the mass matrix can be diagonalized without any artificial
centralization. The shape optimization is performed by the presented
method.
Abstract: A multi-rate discrete-time model, whose response
agrees exactly with that of a continuous-time original at all sampling
instants for any sampling periods, is developed for a linear system,
which is assumed to have multiple real eigenvalues. The sampling
rates can be chosen arbitrarily and individually, so that their ratios
can even be irrational. The state space model is obtained as a
combination of a linear diagonal state equation and a nonlinear output
equation. Unlike the usual lifted model, the order of the proposed
model is the same as the number of sampling rates, which is less than
or equal to the order of the original continuous-time system. The
method is based on a nonlinear variable transformation, which can be
considered as a generalization of linear similarity transformation,
which cannot be applied to systems with multiple eigenvalues in
general. An example and its simulation result show that the proposed
multi-rate model gives exact responses at all sampling instants.
Abstract: The use of the mechanical simulation (in particular the finite element analysis) requires the management of assumptions in order to analyse a real complex system. In finite element analysis (FEA), two modeling steps require assumptions to be able to carry out the computations and to obtain some results: the building of the physical model and the building of the simulation model. The simplification assumptions made on the analysed system in these two steps can generate two kinds of errors: the physical modeling errors (mathematical model, domain simplifications, materials properties, boundary conditions and loads) and the mesh discretization errors. This paper proposes a mesh adaptive method based on the use of an h-adaptive scheme in combination with an error estimator in order to choose the mesh of the simulation model. This method allows us to choose the mesh of the simulation model in order to control the cost and the quality of the finite element analysis.