Abstract: A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.
Abstract: The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.
Abstract: An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.
Abstract: This article is devoted to the numerical solution of
large-scale quadratic eigenvalue problems. Such problems arise in
a wide variety of applications, such as the dynamic analysis of
structural mechanical systems, acoustic systems, fluid mechanics,
and signal processing. We first introduce a generalized second-order
Krylov subspace based on a pair of square matrices and two initial
vectors and present a generalized second-order Arnoldi process for
constructing an orthonormal basis of the generalized second-order
Krylov subspace. Then, by using the projection technique and the
refined projection technique, we propose a restarted generalized
second-order Arnoldi method and a restarted refined generalized
second-order Arnoldi method for computing some eigenpairs of largescale
quadratic eigenvalue problems. Some theoretical results are also
presented. Some numerical examples are presented to illustrate the
effectiveness of the proposed methods.
Abstract: By the application of an improved back-propagation
neural network (BPNN), a model of current densities for a solid oxide
fuel cell (SOFC) with 10 layers is established in this study. To build
the learning data of BPNN, Taguchi orthogonal array is applied to
arrange the conditions of operating parameters, which totally 7 factors
act as the inputs of BPNN. Also, the average current densities
achieved by numerical method acts as the outputs of BPNN.
Comparing with the direct solution, the learning errors for all learning
data are smaller than 0.117%, and the predicting errors for 27
forecasting cases are less than 0.231%. The results show that the
presented model effectively builds a mathematical algorithm to predict
performance of a SOFC stack immediately in real time.
Also, the calculating algorithms are applied to proceed with the
optimization of the average current density for a SOFC stack. The
operating performance window of a SOFC stack is found to be
between 41137.11 and 53907.89. Furthermore, an inverse predicting
model of operating parameters of a SOFC stack is developed here by
the calculating algorithms of the improved BPNN, which is proved to
effectively predict operating parameters to achieve a desired
performance output of a SOFC stack.
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: Due to increased number of terrorist attacks in recent years, loads induced by explosions need to be incorporated in building designs. For safer performance of a structure, its foundation should have sufficient strength and stability. Therefore, prior to any reconstruction or rehabilitation of a building subjected to blast, it is important to examine adverse effects on the foundation caused by blast induced ground shocks. This paper evaluates the effects of a buried explosion on a pile foundation. It treats the dynamic response of the pile in saturated sand, using explicit dynamic nonlinear finite element software LS-DYNA. The blast induced wave propagation in the soil and the horizontal deformation of pile are presented and the results are discussed. Further, a parametric study is carried out to evaluate the effect of varying the explosive shape on the pile response. This information can be used to evaluate the vulnerability of piled foundations to credible blast events as well as develop guidance for their design.
Abstract: The present work is motivated by the idea that the
layer deformation in anisotropic elasticity can be estimated from the
theory of interfacial dislocations. In effect, this work which is an
extension of a previous approach given by one of the authors
determines the anisotropic displacement fields and the critical
thickness due to a complex biperiodic network of MDs lying just
below the free surface in view of the arrangement of dislocations.
The elastic fields of such arrangements observed along interfaces
play a crucial part in the improvement of the physical properties of
epitaxial systems. New results are proposed in anisotropic elasticity
for hexagonal networks of MDs which contain intrinsic and extrinsic
stacking faults. We developed, using a previous approach based on
the relative interfacial displacement and a Fourier series formulation
of the displacement fields, the expressions of elastic fields when
there is a possible dissociation of MDs. The numerical investigations
in the case of the observed system Si/(111)Si with low twist angles
show clearly the effect of the anisotropy and thickness when the
misfit networks are dissociated.
Abstract: Molecular dynamics simulation of annular flow
boiling in a nanochannel with 70000 particles is numerically
investigated. In this research, an annular flow model is developed to
predict the superheated flow boiling heat transfer characteristics in a
nanochannel. To characterize the forced annular boiling flow in a
nanochannel, an external driving force F ext ranging from 1to12PN
(PN= Pico Newton) is applied along the flow direction to inlet fluid
particles during the simulation. Based on an annular flow model
analysis, it is found that saturation condition and superheat degree
have great influences on the liquid-vapor interface. Also, the results
show that due to the relatively strong influence of surface tension in
small channel, the interface between the liquid film and vapor core is
fairly smooth, and the mean velocity along the stream-wise direction
does not change anymore.
Abstract: In this paper, the effect of bolt clamping force on the fatigue behavior of bolted single lap joints of aluminum alloy 2024- T3 have been studied using numerical finite element method. To do so, a three dimensional model according to the bolted single lap joint has been created and numerical analysis has been carried out using finite element based package. Then the stress distribution and also the slip amplitudes have been calculated in the critical regions and the outcome have been compared with the available experimental fatigue tests results. The numerical results show that in low applied clamping force, the fatigue failure of the specimens occur around the stress concentration location (the bolted hole edge) due to the tensile stresses and thus fatigue crack propagation, but with increase of the clamping force, the fatigue life increases and the cracks nucleate and propagate far from the hole edge because of fretting fatigue. In other words, with the further increase of clamping force value of the joint, the fatigue life reduces due to occurrence of the fretting fatigue in the critical location where the slip amplitude is within its critical occurs earlier.
Abstract: In this paper a new embedded Singly Diagonally
Implicit Runge-Kutta Nystrom fourth order in fifth order method for
solving special second order initial value problems is derived. A
standard set of test problems are tested upon and comparisons on the
numerical results are made when the same set of test problems are
reduced to first order systems and solved using the existing
embedded diagonally implicit Runge-Kutta method. The results
suggests the superiority of the new method.
Abstract: Stresses for the elastic-plastic transition and fully
plastic state have been derived for a thin rotating disc with inclusion
and results have been discussed numerically and depicted graphically.
It has been observed that the rotating disc with inclusion and made of
compressible material requires lesser angular speed to yield at the
internal surface whereas it requires higher percentage increase in
angular speed to become fully plastic as compare to disc made of
incompressible material.
Abstract: The sand production problem has led researchers into making various attempts to understand the phenomenon. The generally accepted concept is that the occurrence of sanding is due to the in-situ stress conditions and the induced changes in stress that results in the failure of the reservoir sandstone during hydrocarbon production from wellbores. By using a hypothetical cased (perforated) well, an approach to the problem is presented here by using Finite Element numerical modelling techniques. In addition to the examination of the erosion problem, the influence of certain key parameters is studied in order to ascertain their effect on the failure and subsequent erosion process. The major variables investigated include: drawdown, perforation depth, and the erosion criterion. Also included is the determination of the optimal mud pressure for given operational and reservoir conditions. The improved understanding between parameters enables the choice of optimal values to minimize sanding during oil production.
Abstract: The aeration process via injectors is used to combat
the lack of oxygen in lakes due to eutrophication. A 3D numerical
simulation of the resulting flow using a simplified model is presented.
In order to generate the best dynamic in the fluid with respect to
the aeration purpose, the optimization of the injectors location is
considered. We propose to adapt to this problem the topological
sensitivity analysis method which gives the variation of a criterion
with respect to the creation of a small hole in the domain. The main
idea is to derive the topological sensitivity analysis of the physical
model with respect to the insertion of an injector in the fluid flow
domain. We propose in this work a topological optimization algorithm
based on the studied asymptotic expansion. Finally we present some
numerical results, showing the efficiency of our approach
Abstract: The Goursat partial differential equation arises in
linear and non linear partial differential equations with mixed
derivatives. This equation is a second order hyperbolic partial
differential equation which occurs in various fields of study such as
in engineering, physics, and applied mathematics. There are many
approaches that have been suggested to approximate the solution of
the Goursat partial differential equation. However, all of the
suggested methods traditionally focused on numerical differentiation
approaches including forward and central differences in deriving the
scheme. An innovation has been done in deriving the Goursat partial
differential equation scheme which involves numerical integration
techniques. In this paper we have developed a new scheme to solve
the Goursat partial differential equation based on the Adomian
decomposition (ADM) and associated with Boole-s integration rule to
approximate the integration terms. The new scheme can easily be
applied to many linear and non linear Goursat partial differential
equations and is capable to reduce the size of computational work.
The accuracy of the results reveals the advantage of this new scheme
over existing numerical method.
Abstract: The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.
Abstract: In this paper, an effective sliding mode design is
applied to chaos synchronization. The proposed controller can make
the states of two identical modified Chua-s circuits globally
asymptotically synchronized. Numerical results are provided to show
the effectiveness and robustness of the proposed method.
Abstract: This is a study on numerical simulation of the convection-diffusion transport of a chemical species in steady flow through a small-diameter tube, which is lined with a very thin layer made up of retentive and absorptive materials. The species may be subject to a first-order kinetic reversible phase exchange with the wall material and irreversible absorption into the tube wall. Owing to the velocity shear across the tube section, the chemical species may spread out axially along the tube at a rate much larger than that given by the molecular diffusion; this process is known as dispersion. While the long-time dispersion behavior, well described by the Taylor model, has been extensively studied in the literature, the early development of the dispersion process is by contrast much less investigated. By early development, that means a span of time, after the release of the chemical into the flow, that is shorter than or comparable to the diffusion time scale across the tube section. To understand the early development of the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Flux Corrected Transport Algorithm (FCTA). The computation has enabled us to investigate the combined effects on the early development of the dispersion coefficient due to the reversible and irreversible wall reactions. One of the results is shown that the dispersion coefficient may approach its steady-state limit in a short time under the following conditions: (i) a high value of Damkohler number (say Da ≥ 10); (ii) a small but non-zero value of absorption rate (say Γ* ≤ 0.5).
Abstract: For many chemical and biological processes, the understanding of the mixing phenomenon and flow behavior in a stirred tank is of major importance. A three-dimensional numerical study was performed using the software Fluent, to study the flow field in a stirred tank with a Rushton turbine. In this work, we first studied the flow generated in the tank with a Rushton turbine. Then, we studied the effect of the variation of turbine’s submergence on the thermodynamic quantities defining the flow field. For that, four submergences were considered, while maintaining the same rotational speed (N =250rpm). This work intends to optimize the aeration performances of a Rushton turbine in a stirred tank.
Abstract: Three dimensional simulations in tube in tube heat
exchangers are investigated numerically in this study. In these
simulations forced convective heat transfer and laminar flow of
single-phase water are considered. In order to measure heat transfer
parameters in these heat exchangers, FLUENT CFD Solver is used in
this numerical method. For the purpose of creating geometry and
exert boundary and initial conditions in the present model, finite
volume method in Computational Fluid Dynamics is used in this
study. In the present study, at each Z-location, variation of local
temperatures, heat flux and Nusselt number at the whole tube is
investigated in detail. Thereafter, averaged computational Nusselt
number in this model is calculated. In addition, conceivable pressure
drops have been obtained at each Z-location in this model. Then,
pressure drop values in the present model are explored. Finally, all
the numerical results for this kind of heat exchanger will be discussed
precisely.