Abstract: A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.
Abstract: In this paper, a PSO-based approach is proposed to
derive a digital controller for redesigned digital systems having an interval plant based on resemblance of the extremal gain/phase
margins. By combining the interval plant and a controller as an interval system, extremal GM/PM associated with the loop transfer function
can be obtained. The design problem is then formulated as an optimization problem of an aggregated error function revealing the deviation on the extremal GM/PM between the redesigned digital
system and its continuous counterpart, and subsequently optimized by
a proposed PSO to obtain an optimal set of parameters for the digital controller. Computer simulations have shown that frequency
responses of the redesigned digital system having an interval plant bare a better resemblance to its continuous-time counter part by the incorporation of a PSO-derived digital controller in comparison to those obtained using existing open-loop discretization methods.
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: Three dimensional analysis of thermal model in laser
full penetration welding, Nd:YAG, by transparent mode DP600 alloy
steel 1.25mm of thickness and gap of 0.1mm. Three models studied
the influence of thermal dependent temperature properties, thermal
independent temperature and the effect of peak value of specific heat
at phase transformation temperature, AC1, on the transient
temperature. Another seven models studied the influence of
discretization, meshes on the temperature distribution in weld plate.
It is shown that for the effects of thermal properties, the errors less
4% of maximum temperature in FZ and HAZ have identified. The
minimum value of discretization are at least one third increment per
radius for temporal discretization and the spatial discretization
requires two elements per radius and four elements through thickness
of the assembled plate, which therefore represent the minimum
requirements of modeling for the laser welding in order to get
minimum errors less than 5% compared to the fine mesh.
Abstract: Experimental data from an atmospheric air/water terrain slugging case has been made available by the Shell Amsterdam research center, and has been subject to numerical simulation and comparison with a one-dimensional two-phase slug tracking simulator under development at the Norwegian University of Science and Technology. The code is based on tracking of liquid slugs in pipelines by use of a Lagrangian grid formulation implemented in Cµ by use of object oriented techniques. An existing hybrid spatial discretization scheme is tested, in which the stratified regions are modelled by the two-fluid model. The slug regions are treated incompressible, thus requiring a single momentum balance over the whole slug. Upon comparison with the experimental data, the period of the simulated severe slugging cycle is observed to be sensitive to slug generation in the horizontal parts of the system. Two different slug initiation methods have been tested with the slug tracking code, and grid dependency has been investigated.
Abstract: In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.
Abstract: In a previous work, we presented the numerical
solution of the two dimensional second order telegraph partial
differential equation discretized by the centred and rotated five-point
finite difference discretizations, namely the explicit group (EG) and
explicit decoupled group (EDG) iterative methods, respectively. In
this paper, we utilize a domain decomposition algorithm on these
group schemes to divide the tasks involved in solving the same
equation. The objective of this study is to describe the development
of the parallel group iterative schemes under OpenMP programming
environment as a way to reduce the computational costs of the
solution processes using multicore technologies. A detailed
performance analysis of the parallel implementations of points and
group iterative schemes will be reported and discussed.
Abstract: The effects of dynamic subgrid scale (SGS) models are
investigated in variational multiscale (VMS) LES simulations of bluff
body flows. The spatial discretization is based on a mixed finite
element/finite volume formulation on unstructured grids. In the VMS
approach used in this work, the separation between the largest and the
smallest resolved scales is obtained through a variational projection
operator and a finite volume cell agglomeration. The dynamic version
of Smagorinsky and WALE SGS models are used to account for
the effects of the unresolved scales. In the VMS approach, these
effects are only modeled in the smallest resolved scales. The dynamic
VMS-LES approach is applied to the simulation of the flow around a
circular cylinder at Reynolds numbers 3900 and 20000 and to the flow
around a square cylinder at Reynolds numbers 22000 and 175000. It
is observed as in previous studies that the dynamic SGS procedure
has a smaller impact on the results within the VMS approach than in
LES. But improvements are demonstrated for important feature like
recirculating part of the flow. The global prediction is improved for
a small computational extra cost.
Abstract: This paper presents an improved image segmentation
model with edge preserving regularization based on the
piecewise-smooth Mumford-Shah functional. A level set formulation
is considered for the Mumford-Shah functional minimization in
segmentation, and the corresponding partial difference equations are
solved by the backward Euler discretization. Aiming at encouraging
edge preserving regularization, a new edge indicator function is
introduced at level set frame. In which all the grid points which is used
to locate the level set curve are considered to avoid blurring the edges
and a nonlinear smooth constraint function as regularization term is
applied to smooth the image in the isophote direction instead of the
gradient direction. In implementation, some strategies such as a new
scheme for extension of u+ and u- computation of the grid points and
speedup of the convergence are studied to improve the efficacy of the
algorithm. The resulting algorithm has been implemented and
compared with the previous methods, and has been proved efficiently
by several cases.
Abstract: Many supervised induction algorithms require discrete
data, even while real data often comes in a discrete
and continuous formats. Quality discretization of continuous
attributes is an important problem that has effects on speed,
accuracy and understandability of the induction models. Usually,
discretization and other types of statistical processes are applied
to subsets of the population as the entire population is practically
inaccessible. For this reason we argue that the discretization
performed on a sample of the population is only an estimate of
the entire population. Most of the existing discretization methods,
partition the attribute range into two or several intervals using
a single or a set of cut points. In this paper, we introduce a
technique by using resampling (such as bootstrap) to generate
a set of candidate discretization points and thus, improving the
discretization quality by providing a better estimation towards
the entire population. Thus, the goal of this paper is to observe
whether the resampling technique can lead to better discretization
points, which opens up a new paradigm to construction of
soft decision trees.
Abstract: In this paper, collocation based cubic B-spline and
extended cubic uniform B-spline method are considered for
solving one-dimensional heat equation with a nonlocal initial
condition. Finite difference and θ-weighted scheme is used for
time and space discretization respectively. The stability of the
method is analyzed by the Von Neumann method. Accuracy of
the methods is illustrated with an example. The numerical results
are obtained and compared with the analytical solutions.
Abstract: This paper proposes, implements and evaluates an original discretization method for continuous random variables, in order to estimate the reliability of systems for which stress and strength are defined as complex functions, and whose reliability is not derivable through analytic techniques. This method is compared to other two discretizing approaches appeared in literature, also through a comparative study involving four engineering applications. The results show that the proposal is very efficient in terms of closeness of the estimates to the true (simulated) reliability. In the study we analyzed both a normal and a non-normal distribution for the random variables: this method is theoretically suitable for each parametric family.
Abstract: This paper focuses on a technique for identifying the geological boundary of the ground strata in front of a tunnel excavation site using the first order adjoint method based on the optimal control theory. The geological boundary is defined as the boundary which is different layers of elastic modulus. At tunnel excavations, it is important to presume the ground situation ahead of the cutting face beforehand. Excavating into weak strata or fault fracture zones may cause extension of the construction work and human suffering. A theory for determining the geological boundary of the ground in a numerical manner is investigated, employing excavating blasts and its vibration waves as the observation references. According to the optimal control theory, the performance function described by the square sum of the residuals between computed and observed velocities is minimized. The boundary layer is determined by minimizing the performance function. The elastic analysis governed by the Navier equation is carried out, assuming the ground as an elastic body with linear viscous damping. To identify the boundary, the gradient of the performance function with respect to the geological boundary can be calculated using the adjoint equation. The weighed gradient method is effectively applied to the minimization algorithm. To solve the governing and adjoint equations, the Galerkin finite element method and the average acceleration method are employed for the spatial and temporal discretizations, respectively. Based on the method presented in this paper, the different boundary of three strata can be identified. For the numerical studies, the Suemune tunnel excavation site is employed. At first, the blasting force is identified in order to perform the accuracy improvement of analysis. We identify the geological boundary after the estimation of blasting force. With this identification procedure, the numerical analysis results which almost correspond with the observation data were provided.
Abstract: The problem addressed herein is the efficient management of the Grid/Cluster intense computation involved, when the preconditioned Bi-CGSTAB Krylov method is employed for the iterative solution of the large and sparse linear system arising from the discretization of the Modified Helmholtz-Dirichlet problem by the Hermite Collocation method. Taking advantage of the Collocation ma-trix's red-black ordered structure we organize efficiently the whole computation and map it on a pipeline architecture with master-slave communication. Implementation, through MPI programming tools, is realized on a SUN V240 cluster, inter-connected through a 100Mbps and 1Gbps ethernet network,and its performance is presented by speedup measurements included.
Abstract: The aim of this paper is to develop a new two dimensional time accurate Euler solver for shock tube applications. The solver was developed to study the performance of a newly built short-duration hypersonic test facility at Universiti Tenaga Nasional “UNITEN" in Malaysia. The facility has been designed, built, and commissioned for different values of diaphragm pressure ratios in order to get wide range of Mach number. The developed solver uses second order accurate cell-vertex finite volume spatial discretization and forth order accurate Runge-Kutta temporal integration and it is designed to simulate the flow process for similar driver/driven gases (e.g. air-air as working fluids). The solver is validated against analytical solution and experimental measurements in the high speed flow test facility. Further investigations were made on the flow process inside the shock tube by using the solver. The shock wave motion, reflection and interaction were investigated and their influence on the performance of the shock tube was determined. The results provide very good estimates for both shock speed and shock pressure obtained after diaphragm rupture. Also detailed information on the gasdynamic processes over the full length of the facility is available. The agreements obtained have been reasonable.
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: A parallel computational fluid dynamics code has been
developed for the study of aerodynamic heating problem in hypersonic
flows. The code employs the 3D Navier-Stokes equations as the basic
governing equations to simulate the laminar hypersonic flow. The cell
centered finite volume method based on structured grid is applied for
spatial discretization. The AUSMPW+ scheme is used for the inviscid
fluxes, and the MUSCL approach is used for higher order spatial
accuracy. The implicit LU-SGS scheme is applied for time integration
to accelerate the convergence of computations in steady flows. A
parallel programming method based on MPI is employed to shorten
the computing time. The validity of the code is demonstrated by
comparing the numerical calculation result with the experimental data
of a hypersonic flow field around a blunt body.
Abstract: Dense slurry flow through centrifugal pump casing
has been modeled using the Eulerian-Eulerian approach with
Eulerian multiphase model in FLUENT 6.1®. First order upwinding
is considered for the discretization of momentum, k and ε terms.
SIMPLE algorithm has been applied for dealing with pressurevelocity
coupling. A mixture property based k-ε turbulence model
has been used for modeling turbulence. Results are validated first
against mesh independence and experiments for a particular set of
operational and geometric conditions. Parametric analysis is then
performed to determine the effect on important physical quantities
viz. solid velocities, solid concentration and solid stresses near the
wall with various operational geometric conditions of the pump.
Abstract: The optimal grid spacing and turbulence model for the
2D numerical analysis of a vertical-axis water turbine (VAWaterT)
operating in a 2 m/s freestream current has been investigated. The
results of five different spatial domain discretizations and two
turbulence models (k-ω SST and k-ε RNG) have been compared, in
order to gain the optimal y+ parameter distribution along the blade
walls during a full rotor revolution. The resulting optimal mesh has
appeared to be quite similar to that obtained for the numerical
analysis of a vertical-axis wind turbine.
Abstract: Saccharomyces cerevisiae (baker-s yeast) can exhibit
sustained oscillations during the operation in a continuous bioreactor
that adversely affects its stability and productivity. Because of
heterogeneous nature of cell populations, the cell population balance
models can be used to capture the dynamic behavior of such cultures.
In this paper an unstructured, segregated model is used which is
based on population balance equation(PBE) and then in order to
simulation, the 4th order Rung-Kutta is used for time dimension and
three methods, finite difference, orthogonal collocation on finite
elements and Galerkin finite element are used for discretization of the
cell mass domain. The results indicate that the orthogonal collocation
on finite element not only is able to predict the oscillating behavior of
the cell culture but also needs much little time for calculations.
Therefore this method is preferred in comparison with other methods.
In the next step two controllers, a globally linearizing control (GLC)
and a conventional proportional-integral (PI) controller are designed
for controlling the total cell mass per unit volume, and performances
of these controllers are compared through simulation. The results
show that although the PI controller has simpler structure, the GLC
has better performance.