Abstract: A strip domain decomposition parallel algorithm for fast direct Poisson solver is presented on a 3D Cartesian staggered grid. The parallel algorithm follows the principles of sequential algorithm for fast direct Poisson solver. Both Dirichlet and Neumann boundary conditions are addressed. Several test cases are likewise addressed in order to shed light on accuracy and efficiency in the strip domain parallelization algorithm. Actually the current implementation shows a very high efficiency when dealing with a large grid mesh up to 3.6 * 109 under massive parallel approach, which explicitly demonstrates that the proposed algorithm is ready for massive parallel computing.
Abstract: In this paper we present our results on the performance analysis of a multi-product manufacturing line. We study the influence of external perturbations, intermediate buffer content and the number of manufacturing stages on the production tracking error of each machine in the multi-product line operated under a surplusbased production control policy. Starting by the analysis of a single machine with multiple production stages (one for each product type), we provide bounds on the production error of each stage. Then, we extend our analysis to a line of multi-stage machines, where similarly, bounds on each production tracking error for each product type, as well as buffer content are obtained. Details on performance of the closed-loop flow line model are illustrated in numerical simulations.
Abstract: For many industrial applications plate heat
exchangers are demonstrating a large superiority over the
other types of heat exchangers. The efficiency of such a
device depends on numerous factors the effect of which needs
to be analysed and accurately evaluated.
In this paper we present a theoretical analysis of a cocurrent
plate heat exchanger and the results of its numerical
simulation.
Knowing the hot and the cold fluid streams inlet temperatures,
the respective heat capacities mCp
and the value of the
overall heat transfer coefficient, a 1-D mathematical model
based on the steady flow energy balance for a differential
length of the device is developed resulting in a set of N first
order differential equations with boundary conditions where N
is the number of channels.For specific heat exchanger
geometry and operational parameters, the problem is
numerically solved using the shooting method.
The simulation allows the prediction of the temperature
map in the heat exchanger and hence, the evaluation of its
performances. A parametric analysis is performed to evaluate
the influence of the R-parameter on the e-NTU values. For
practical purposes effectiveness-NTU graphs are elaborated
for specific heat exchanger geometry and different operating
conditions.
Abstract: The stability characteristics of water lubricated journal bearings having three axial grooves are obtained theoretically. In this lubricant (water) is fed under pressure from one end of the bearing, through the 3-axial grooves (groove angles may vary). These bearings can use the process fluid as the lubricant, as in the case of feed water pumps. The Reynolds equation is solved numerically by the finite difference method satisfying the boundary conditions. The stiffness and damping coefficient for various bearing number and eccentricity ratios, assuming linear pressure drop along the groove, shows that smaller groove angles better results.
Abstract: Calcium [Ca2+] dynamics is studied as a potential form
of neuron excitability that can control many irregular processes like
metabolism, secretion etc. Ca2+ ion enters presynaptic terminal and
increases the synaptic strength and thus triggers the neurotransmitter
release. The modeling and analysis of calcium dynamics in neuron
cell becomes necessary for deeper understanding of the processes
involved. A mathematical model has been developed for cylindrical
shaped neuron cell by incorporating physiological parameters like
buffer, diffusion coefficient, and association rate. Appropriate initial
and boundary conditions have been framed. The closed form solution
has been developed in terms of modified Bessel function. A computer
program has been developed in MATLAB 7.11 for the whole
approach.
Abstract: In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.
Abstract: This paper is concerned with an investigation into the
localized non-stability of a thin elastic orthotropic semi-infinite plate.
In this study, a semi-infinite plate, simply supported on two edges
and different boundary conditions, clamped, hinged, sliding contact
and free on the other edge, are considered. The mathematical model
is used and a general solution is presented the conditions under which
localized solutions exist are investigated.
Abstract: An accurate procedure to determine free vibrations of
beams and plates is presented.
The natural frequencies are exact solutions of governing vibration
equations witch load to a nonlinear homogeny system.
The bilinear and linear structures considered simulate a bridge.
The dynamic behavior of this one is analyzed by using the theory of
the orthotropic plate simply supported on two sides and free on the
two others. The plate can be excited by a convoy of constant or
harmonic loads. The determination of the dynamic response of the
structures considered requires knowledge of the free frequencies and
the shape modes of vibrations. Our work is in this context. Indeed,
we are interested to develop a self-consistent calculation of the Eigen
frequencies.
The formulation is based on the determination of the solution of
the differential equations of vibrations. The boundary conditions
corresponding to the shape modes permit to lead to a homogeneous
system. Determination of the noncommonplace solutions of this
system led to a nonlinear problem in Eigen frequencies.
We thus, develop a computer code for the determination of the
eigenvalues. It is based on a method of bisection with interpolation
whose precision reaches 10 -12. Moreover, to determine the
corresponding modes, the calculation algorithm that we develop uses
the method of Gauss with a partial optimization of the "pivots"
combined with an inverse power procedure. The Eigen frequencies
of a plate simply supported along two opposite sides while
considering the two other free sides are thus analyzed. The results
could be generalized with the case of a beam by regarding it as a
plate with low width.
We give, in this paper, some examples of treated cases. The
comparison with results presented in the literature is completely
satisfactory.
Abstract: Mathematical and computational modeling of calcium
signalling in nerve cells has produced considerable insights into how
the cells contracts with other cells under the variation of biophysical
and physiological parameters. The modeling of calcium signaling in
astrocytes has become more sophisticated. The modeling effort has
provided insight to understand the cell contraction. Main objective
of this work is to study the effect of voltage gated (Operated)
calcium channel (VOC) on calcium profile in the form of advection
diffusion equation. A mathematical model is developed in the form
of advection diffusion equation for the calcium profile. The model
incorporates the important physiological parameter like diffusion
coefficient etc. Appropriate boundary conditions have been framed.
Finite volume method is employed to solve the problem. A program
has been developed using in MATLAB 7.5 for the entire problem
and simulated on an AMD-Turion 32-bite machine to compute the
numerical results.
Abstract: The paper deals with a mathematical model for fluid dynamic flows on road networks which is based on conservation laws. This nonlinear framework is based on the conservation of cars. We focus on traffic circle, which is a finite number of roads that meet at some junctions. The traffic circle with junctions having either one incoming and two outgoing or two incoming and one outgoing roads. We describe the numerical schemes with the particular boundary conditions used to produce approximated solutions of the problem.
Abstract: The Spalart and Allmaras turbulence model has been
implemented in a numerical code to study the compressible turbulent
flows, which the system of governing equations is solved with a
finite volume approach using a structured grid. The AUSM+ scheme
is used to calculate the inviscid fluxes. Different benchmark
problems have been computed to validate the implementation and
numerical results are shown. A special Attention is paid to wall jet
applications. In this study, the jet is submitted to various wall
boundary conditions (adiabatic or uniform heat flux) in forced
convection regime and both two-dimensional and axisymmetric wall
jets are considered. The comparison between the numerical results
and experimental data has given the validity of this turbulence model
to study the turbulent wall jets especially in engineering applications.
Abstract: To achieve accurate and precise results of finite
element analysis (FEA) of bones, it is important to represent the
load/boundary conditions as identical as possible to the human body
such as the bone properties, the type and force of the muscles, the
contact force of the joints, and the location of the muscle attachment.
In this study, the difference in the Von-Mises stress and the total
deformation was compared by classifying them into Case 1, which
shows the actual anatomical form of the muscle attached to the femur
when the same muscle force was applied, and Case 2, which gives a
simplified representation of the attached location. An inverse
dynamical musculoskeletal model was simulated using data from an
actual walking experiment to complement the accuracy of the
muscular force, the input value of FEA. The FEA method using the
results of the muscular force that were calculated through the
simulation showed that the maximum Von-Mises stress and the
maximum total deformation in Case 2 were underestimated by 8.42%
and 6.29%, respectively, compared to Case 1. The torsion energy and
bending moment at each location of the femur occurred via the stress
ingredient. Due to the geometrical/morphological feature of the femur
of having a long bone shape when the stress distribution is wide, as
shown in Case 1, a greater Von-Mises stress and total deformation are
expected from the sum of the stress ingredients. More accurate results
can be achieved only when the muscular strength and the attachment
location in the FEA of the bones and the attachment form are the same
as those in the actual anatomical condition under the various moving
conditions of the human body.
Abstract: This paper is concerned with propagation of thermoelastic longitudinal vibrations of an infinite circular cylinder, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equation, by using the traction free boundary conditions, is given in the form of a determinant involving Bessel functions. The roots of the frequency equation give the value of the characteristic circular frequency as function of the wave number. These roots, which correspond to various modes, are numerically computed and presented graphically for different values of the thermal relaxation times. It is found that the influences of the thermal relaxation times on the amplitudes of the elastic and thermal waves are remarkable. Also, it is shown in this study that the propagation of thermoelastic longitudinal vibrations based on the generalized thermoelasticity can differ significantly compared with the results under the classical formulation. A comparison of the results for the case with no thermal effects shows well agreement with some of the corresponding earlier results.
Abstract: In this study the mixed convection heat transfer in a
coil-in-shell heat exchanger for various Reynolds numbers and
various dimensionless coil pitch was experimentally investigated.
The experiments were conducted for both laminar and turbulent flow
inside coil and the effects of coil pitch on shell-side heat transfer
coefficient of the heat exchanger were studied. The particular
difference in this study in comparison with the other similar studies
was the boundary conditions for the helical coils. The results indicate
that with the increase of coil pitch, shell-side heat transfer coefficient
is increased.
Abstract: A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.
Abstract: Organ motion, especially respiratory motion, is a technical challenge to radiation therapy planning and dosimetry. This motion induces displacements and deformation of the organ tissues within the irradiated region which need to be taken into account when simulating dose distribution during treatment. Finite element modeling (FEM) can provide a great insight into the mechanical behavior of the organs, since they are based on the biomechanical material properties, complex geometry of organs, and anatomical boundary conditions. In this paper we present an original approach that offers the possibility to combine image-based biomechanical models with particle transport simulations. We propose a new method to map material density information issued from CT images to deformable tetrahedral meshes. Based on the principle of mass conservation our method can correlate density variation of organ tissues with geometrical deformations during the different phases of the respiratory cycle. The first results are particularly encouraging, as local error quantification of density mapping on organ geometry and density variation with organ motion are performed to evaluate and validate our approach.
Abstract: The Stokes equation connected with the fluid flow
over the axisymmetric bodies in a cylindrical area is considered. The
equation is studied in a moving coordinate system with the
appropriate boundary conditions. Effective formulas for the velocity
components are obtained. The graphs of the velocity components and
velocity profile are plotted.
Abstract: Different techniques for estimating seasonal water
use from soil profile water depletion frequently do not account for
flux below the root zone. Shallow water table contribution to supply
crop water use may be important in arid and semi-arid regions.
Development of predictive root uptake models, under influence of
shallow water table makes it possible for planners to incorporate
interaction between water table and root zone into design of irrigation
projects. A model for obtaining soil moisture depletion from root
zone and water movement below it is discussed with the objective to
determine impact of shallow water table on seasonal moisture
depletion patterns under water table depth variation, up to the bottom
of root zone. The role of different boundary conditions has also been
considered. Three crops: Wheat (Triticum aestivum), Corn (Zea
mays) and Potato (Solanum tuberosum), common in arid & semi-arid
regions, are chosen for the study. Using experimentally obtained soil
moisture depletion values for potential soil moisture conditions,
moisture depletion patterns using a non linear root uptake model have
been obtained for different water table depths. Comparative analysis
of the moisture depletion patterns under these conditions show a wide
difference in percent depletion from different layers of root zone
particularly top and bottom layers with middle layers showing
insignificant variation in moisture depletion values. Moisture
depletion in top layer, when the water table rises to root zone
increases by 19.7%, 22.9% & 28.2%, whereas decrease in bottom
layer is 68.8%, 61.6% & 64.9% in case of wheat, corn & potato
respectively. The paper also discusses the causes and consequences
of increase in moisture depletion from top layers and exceptionally
high reduction in bottom layer, and the possible remedies for the
same. The numerical model developed for the study can be used to
help formulating irrigation strategies for areas where shallow
groundwater of questionable quality is an option for crop production.
Abstract: In this paper, linear multistep technique using power
series as the basis function is used to develop the block methods
which are suitable for generating direct solution of the special second
order ordinary differential equations with associated initial or
boundary conditions. The continuous hybrid formulations enable us
to differentiate and evaluate at some grids and off – grid points to
obtain two different four discrete schemes, each of order (5,5,5,5)T,
which were used in block form for parallel or sequential solutions of
the problems. The computational burden and computer time wastage
involved in the usual reduction of second order problem into system
of first order equations are avoided by this approach. Furthermore, a
stability analysis and efficiency of the block methods are tested on
linear and non-linear ordinary differential equations and the results
obtained compared favorably with the exact solution.
Abstract: An attempt has been made to develop a
seminumerical model to study temperature variations in dermal
layers of human limbs. The model has been developed for two
dimensional steady state case. The human limb has been assumed to
have elliptical cross section. The dermal region has been divided
into three natural layers namely epidermis, dermis and subdermal
tissues. The model incorporates the effect of important physiological
parameters like blood mass flow rate, metabolic heat generation, and
thermal conductivity of the tissues. The outer surface of the limb is
exposed to the environment and it is assumed that heat loss takes
place at the outer surface by conduction, convection, radiation, and
evaporation. The temperature of inner core of the limb also varies at
the lower atmospheric temperature. Appropriate boundary conditions
have been framed based on the physical conditions of the problem.
Cubic splines approach has been employed along radial direction and
Fourier series along angular direction to obtain the solution. The
numerical results have been computed for different values of
eccentricity resembling with the elliptic cross section of the human
limbs. The numerical results have been used to obtain the
temperature profile and to study the relationships among the various
physiological parameters.