Thermally developing flow in finned double-pipe heat exchanger

Thermally developing flow in finned double-pipe heat exchanger: "A numerical solution of the convective heat transfer in the thermal entry region of the finned double-pipe is carried out for the case of hydro-dynamically fully developed flow when subjected to uniform wall temperature boundary condition. Adaptive axial grid size is used in order to cater for the variation of large solution gradients in the axial direction. It has been observed that the thermal entrance region is highly effective and there is a substantial enhancement in the heat transfer coefficient. A maximum of 76.4877% increase has been observed in the thermal entrance region as compared with the fully developed region for 24 fins and H*=0.6 when [Rcirc]=0.25, whereas for [Rcirc]=0.5 the maximum increase is 75.0308% for the same number of fins of same height. It has been observed that no geometry consistently perform better throughout the entrance region. However, the geometries that have optimal performance in the fully developed region perform better in the developing region on average terms. Results show that the Nusselt number and the thermal entrance length are dependent upon various geometrical parameters such as ratio of radii of the inner and the outer pipe, fin height and the number of fins. The limiting case results match well with the literature results. This validates our numerical procedure and computer code. Copyright © 2010 John Wiley & Sons, Ltd."

Information flux maximum-entropy approximation schemes for convection-diffusion problems

Information flux maximum-entropy approximation schemes for convection-diffusion problems: "The requirement for stabilization or other similar techniques is well known when using the finite element method in computational fluid mechanics. A variety of such techniques has been introduced during the past decades along with different physical interpretations of the stabilization terms employed. In introducing so-called information flux methods, we developed a new point of view on the problem of numerical instabilities; with respect to Shannon's information theory instabilities are interpreted as a consequence of unadequate observance of the information flux present in fluid mechanics. Here we discuss different approaches to setting up information flux maximum-entropy approximation schemes based on that idea. The good accuracy of these approximation schemes is demonstrated for convection-diffusion problems by means of several linear, time-independent one- and two-dimensional numerical examples and comparisons with state-of-the-art stabilized finite element methods. Copyright © 2010 John Wiley & Sons, Ltd."

A Direct Solver for the Rapid Solution of Boundary Integral Equations on Axisymmetric Surfaces in Three Dimensions. (arXiv:1002.2001v1 [math.NA])

A Direct Solver for the Rapid Solution of Boundary Integral Equations on Axisymmetric Surfaces in Three Dimensions. (arXiv:1002.2001v1 [math.NA]): "

A scheme for rapidly and accurately computing solutions to boundary integral
equations (BIEs) on rotationally symmetric surfaces in three dimensions is
presented. The scheme uses the Fourier transform to reduce the original BIE
defined on a surface to a sequence of BIEs defined on a generating curve for
the surface. It can handle loads that are not necessarily rotationally
symmetric. Nystrom discretization is used to discretize the BIEs on the
generating curve. The quadrature used is a high-order Gaussian rule that is
modified near the diagonal to retain high-order accuracy for singular kernels.
The reduction in dimensionality, along with the use of high-order accurate
quadratures, leads to small linear systems that can be inverted directly via,
e.g., Gaussian elimination. This makes the scheme particularly fast in
environments involving multiple right hand sides. It is demonstrated that for
BIEs associated with Laplace's equation, the kernel in the reduced equations
can be evaluated very rapidly by exploiting recursion relations for Legendre
functions. Numerical examples illustrate the performance of the scheme; in
particular, it is demonstrated that for a BIE associated with Laplace's
equation on a surface discretized using 320 000 points, the set-up phase of the
algorithm takes 2 minutes on a standard desktop, and then solves can be
executed in 0.5 seconds.

"

The Mystery of the Shape Parameter II. (arXiv:1002.2082v1 [math.NA])

The Mystery of the Shape Parameter II. (arXiv:1002.2082v1 [math.NA]): "

In this paper we present criteria for the choice of the shape parameter c
contained in the famous radial function multiquadric. It may be of interest to
RBF people and all people using radial basis functions to do approximation.

"

Efficient component-wise and solver-based intrusive SFEM analysis of complex structures

Efficient component-wise and solver-based intrusive SFEM analysis of complex structures: "Publication year: 2010
Source: Finite Elements in Analysis and Design, In Press, Corrected Proof, Available online 9 February 2010
H.M., Panayirci , M.F., Pellissetti
In this study, important computational aspects of intrusive stochastic finite element methods (SFEM) are investigated. The importance of the interaction with 3rd party deterministic finite element (FE) solvers is emphasized within this context. Especially, data management is in the focus. Two implementation techniques, namely the component-wise and the solver-based implementations, have been introduced in order to improve the computational efficiency. It is shown that by reducing the quantity and the size of the transferred system matrices, a significant reduction in the computational cost can be achieved. This is demonstrated on representative FE models, which are analyzed with the perturbation method,..."

An enriched discontinuous Galerkin formulation for the coupling of non-conforming meshes

An enriched discontinuous Galerkin formulation for the coupling of non-conforming meshes: "Publication year: 2010
Source: Finite Elements in Analysis and Design, In Press, Corrected Proof, Available online 9 February 2010
G., Haikal , K.D., Hjelmstad
Finite element modeling using non-conforming meshes requires an interface model that ensures geometric compatibility and a complete transfer of surface tractions between the connecting elements at the non-conforming interfaces. Most currently available coupling methods are dual approaches that employ a field of Lagrange multipliers to enforce geometric compatibility at the interface. The choice of the Lagrange multiplier field is not trivial since not all possible interpolations satisfy the inf–sup or Ladyzhenskaya–Babuška-Brezzi (LBB) condition. The primal discontinuous Galerkin (DG) and Nitsche methods are not subject to the LBB restrictions, however, in both these methods a mesh-dependent penalty parameter is required to..."

Natural and artificial atoms for quantum computation. (arXiv:1002.1871v1 [quant-ph])

Natural and artificial atoms for quantum computation. (arXiv:1002.1871v1 [quant-ph]): "

Remarkable progress towards realizing quantum computation has been achieved
using natural and artificial atoms. On the one hand, natural atoms (such as
neutral atoms and ions) have long coherence times, and could be stored in large
arrays, providing ideal 'quantum memories'. On the other hand, artificial atoms
(such as superconducting circuits or semiconductor quantum dots) have the
advantage of custom-designed features and could be used as 'quantum processing
units'. Natural and artificial atoms can be coupled with each other and can
also be interfaced with photons for long-distance communications. Hybrid
devices made of natural/artificial atoms and photons may provide the
next-generation design for quantum computers.

"

Algebraic multilevel iteration methods and the best approximation to $1/x$ in the uniform norm. (arXiv:1002.1859v1 [math.NA])

Algebraic multilevel iteration methods and the best approximation to $1/x$ in the uniform norm. (arXiv:1002.1859v1 [math.NA]): "

In this note, we provide simple convergence analysis for the algebraic
multilevel iteration methods. We consider two examples of AMLI methods with
different polynomial acceleration. The first one is based on shifted and scaled
Chebyshev polynomial and the other on the polynomial of best approximation to
$x^{-1}$ on a finite interval with positive endpoints in the uniform norm. The
construction of the latter polynomial is of interest by itself, and we have
included a derivation of a 3 term recurrence relation for computing this
polynomial. We have also derived several inequalities related to the error of
best approximation, which we applied in the AMLI analysis.

"

Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra. (arXiv:1002.1772v1 [math.AP])

Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra. (arXiv:1002.1772v1 [math.AP]): "

We prove weighted anisotropic analytic estimates for solutions of model
elliptic boundary value problems in polyhedra. The weighted analytic classes
which we use are the same as those introduced by B. Guo in 1993 in view of
establishing exponential convergence for hp methods in polyhedra. We first give
a simple proof of the weighted analytic regularity in a polygon, relying on new
elliptic a priori estimates with analytic control of derivatives in smooth
domains. The technique is based on dyadic partitions near the corners. This
technique can be successfully extended to polyhedra, but only isotropic
analytic regularity can be proved in this way. We therefore combine it with a
nested open set technique to obtain the three-dimensional anisotropic analytic
result. Our proofs are global and do not rely on the analysis of singularities.

"