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Numerical Simulations
Get PDFThis book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation
Numerical Simulations
No full textThis book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation
Ein mehrskalen- und dualitätsbasiertes Viskositätsmodell für die inkompressiblen Navier-Stokes-Gleichungen
Get PDFEine wichtige Anwendung in den Ingenieurwissenschaften und in der Physik ist die Berechnung
der Strömung von Flüssigkeiten oder Gasen. Das Verhalten solcher Fluide wird häufig durch die
Navier-Stokes-Gleichungen beschrieben. Viele dieser Probleme lassen sich nicht analytisch lösen,
sondern nur numerisch approximieren. Insbesondere bei turbulenten Strömungen besteht die
Schwierigkeit, dass die Diskretisierung nicht alle Skalen auflösen kann. Kleine Verwirbelungen
können somit nicht berechnet werden. Üblicherweise werden ihre Effekte jedoch mithilfe von
Subgrid-Modellen nachgebildet. Diese Techniken sind auch als Large Eddy Simulation oder
variationelle Multiskalenmethode bekannt. Viele der Subgrid-Modelle gehen als zusätzliche
Diffusion in Form einer künstlichen Viskosität in die Differentialgleichungen ein, es wird von
Reynolds-Averaged-Navier-Stokes-Gleichungen gesprochen.
Moderne Verfahren zur numerischen Lösung von Differentialgleichungen verändern die der
Diskretisierung zugrunde liegenden Gitter in Abhängigkeit von der zu bestimmenden Lösung.
Als Indikator für eine adaptive Gitterverfeinerung kann ein Funktional der Lösung verwendet
werden. Dieses Funktional wird im Vorfeld vom Anwender vorgegeben und beschreibt eine
Größe, die ihm bei der Approximation besonders wichtig ist. Mithilfe eines dualen Problems
können dann die Gitterelemente identifiziert werden, bei denen eine lokale Änderung der
Lösung einen besonders großen Ein
uss auf den Wert des Funktionals hat. Bei der verbreiteten
Technik der Dual Weighted Residuals werden gezielt diese Gitterelemente verfeinert.
In der vorliegenden Arbeit wird auf Grundlage einer a-posteriori-Fehlerabschätzung ein inverses
Problem entwickelt, das die künstliche Viskosität nicht als Parameter, sondern als Variable
enthält. Statt aus einer vorgegebenen künstlichen Viskosität die resultierende Strömung zu
berechnen, wird diejenige künstliche Viskosität gesucht, die eine Strömung liefert, deren
Funktionalwert möglichst exakt ist. Es wird ein mehrskaliger Ansatz verwendet, um den
Funktionalwert einer feineren Diskretisierung als Referenz nutzen zu können.
Auf Grundlage dieser neuen Idee kann für beliebige (partielle) Differentialgleichungen mitsamt
eines vorgegebenen Modellierungsansatzes ein solches inverses Problem formuliert werden.
Die Lösung des inversen Problems steuert dabei den Modellierungsansatz in Raum und Zeit.
Anschließend wird das resultierende System aus fünf Variationsgleichungen im konkreten
Kontext der instationären inkompressiblen Navier-Stokes-Gleichungen formuliert, auf Basis
der Finite-Elemente-Methode implementiert und anhand von drei Modellproblemen praktisch
gelöst.
Schließlich wird noch der Frage nachgegangen, ob und wie aus der so gewonnenen konkreten
künstlichen Viskosität wieder ein (allgemeiner verwendbares) Viskositätsmodell konstruiert
werden kann. Dazu werden Approximationsansätze auf Grundlage von reduzierten Basen,
nichtlinearer Approximation sowie radialen Basisfunktionen diskutiert, implementiert und auf
die vorgestellten Modellprobleme angewendet. Diese neuen Viskositätsmodelle werden mit den
bereits gewonnenen Daten verglichen und eingeordnet.The calculation of the flow of liquids or gases is an important application in engineering and physics. The behavior of such fluids is often expressed by means of the Navier-Stokes equations.
Many of these problems can not be solved analytically, but only approximated numerically. Particularly for turbulent flows, one experiences the diffculty that the discretization can not resolve all scales. Therefore small eddies can not be calculated. Usually, their effects are replicated using subgrid models. These techniques are also known as large eddy simulation or variational multiscale method. Many of the subgrid models act as an additional diffusion in the form of an artificial viscosity in the differential equations which are called Reynolds-averaged Navier-Stokes equations.
Modern methods for the numerical solution of differential equations change the underlying grid of the discretization depending on the solution to be determined. A functional of the
solution can be used as an indicator for this adaptive mesh refinement.
This functional is given in advance by the user and describes an entity which is particularly important to him or her in the approximation. Using a dual problem, those grid elements can
then be identified, where a local change of the solution has a particularly large impact on the value of the functional. In the widespread technique of dual weighted residuals these grid
elements are then refined specifically.
In this work an inverse problem is developed, which is based on an a posteriori error estimate, and which does not use the artificial viscosity as a parameter, but as a variable. Instead of
using a predetermined artificial viscosity in order to calculate the resulting flow, we search for an artificial viscosity, which provides a flow with the most accurate functional value. A multi-scale approach is applied in order to use the functional value of a finer discretization as a reference.
Based on this new idea such an inverse problem can be formulated for any (partial) differential equations together with a given modeling approach. The solution of the inverse problem
thereby controls the modeling approach in space and time. Subsequently, the resulting system of five variational equations is formulated in the specific context of the unsteady incompressible
Navier-Stokes equations, implemented based on the finite element method and practically solved for three model problems.
Finally, the question is posed, whether and how to obtain a (general-purpose) viscosity model from this concrete artificial viscosity. Approaches for an approximation based on reduced bases, nonlinear approximation and radial basis functions are discussed implemented and applied to the presented model problems. These new viscosity models are compared and classified to the data already collected
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity
Get PDFThe present work describes some extensions of an approach, originally
developed by V.V. Yatsyk and the author, for the theoretical and numerical
analysis of scattering and radiation effects on infinite plates with cubically
polarized layers. The new aspects lie on the transition to more generally
shaped, two- or three-dimensional objects, which no longer necessarily have to
be represented in terms a Cartesian product of real intervals, to more general
nonlinearities (including saturation) and the possibility of an efficient
numerical approximation of the electromagnetic fields and derived quantities
(such as energy, transmission coefficient, etc.). The paper advocates an
approach that consists in transforming the original full-space problem for a
nonlinear Helmholtz equation (as the simplest model) into an equivalent
boundary-value problem on a bounded domain by means of a nonlocal
Dirichlet-to-Neumann (DtN) operator. It is shown that the transformed problem
is equivalent to the original one and can be solved uniquely under suitable
conditions. Morever, the impact of the truncation of the DtN operator on the
resulting solution is investigated, so that the way to the numerical solution
by appropriate finite element methods is available
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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