13 documents found

Dissertation
All rights reserved
2017-08-01

Entwurf und Programmierung von numerischen Verfahren und Algorithmen zur...

Die Boltzmann-Gleichung ist eine mesoskopische Gleichung, welche Gas-Strömungen im Übergang zur Teilchendynamik beschreibt. Die Methoden zur Lösung der Boltzmann Gleichung sind ein wichtiges Forschungsthema. In dieser Arbeit interessieren wir uns für die sogenannten deterministischen Schemata, die mit...
Article / Chapter
All rights reserved
2015-11-12

Macroscopic limit for an evaporation-condensation problem

We consider a rarefied gas mixture confined between two parallel walls consisting of vapor passing through the walls (evaporation, condensation), and a noncondensable which is totally reflected at the walls. Under a diffusive scaling we derive a macroscopic limit in which the noncondensable forms a well-defined...
Dissertation
2015-07-09

Classification of Lattice Group Models, High Order Discretizations of Boltzmann’s...

´╗┐In dieser Arbeit geht es um Gittergruppenmodelle (LGpMs). Hierbei handelt es sich um eine Klasse von deterministischen Diskretisierungsmodellen, welche offenbar mit diskreten Geschwindigkeitsmodellen (DVMs) in Verbindung stehen. Unglücklicherweise existieren für die Diskretisierung des Kollisionsoperators...
Article / Chapter
All rights reserved
2012-10-25

Discrete kinetic models in the fluid dynamic limit

We investigate discrete kinetic models in the Fluid dynamic limit described by the Euler system and the Navier-Stokes correction obtained by the Chapman Enskog procedure. We show why reliable "small" systems can be expected only for small Mach numbers and derive a calculus for designing models for given...
Book
All rights reserved
2011-02-17

Numerische Approximation von Funktionen

In der vorliegenden Arbeit, die auf der Basis einer Vorlesung in der Ausbildung von Ingenieuren und Informatikern an der TU Ilmenau entstand, werden Aspekte der Approximation mittels Bézier-Kurven und Splines für Kurven und Flächen behandelt. Sie spielen beim rechnerunterstützten Entwerfen (Computer...
Diploma thesis
2009-10-08

Numerische Verfolgung von Gleichgewichtslagen dynamischer Systeme- Stabilitätsanalyse...

By setting the parameters of the program, you can even choose exactly how and how effectively the curves are to be determined. In various examples, the possibilities were tested adjustment parameters to define a stability in the program.
Dissertation
2009-07-31

Distributional differential algebraic equations

Trenn, Stephan:Distributional differential algebraic equations(Zusammenfassung, Diss., Technische Universität Ilmenau, 2009) Lineare implizite Differentialgleichungen der Form Ex'=Ax+f werden untersucht. Da die Matrix E nicht als invertierbar angenommen wird, enthält das Gleichungssystem neben...
Article / Chapter
All rights reserved
2009-01-30

A numerical model for the Boltzmann equation with applications to micro...

Given an integer lattice \mathcal{L} \subset \mathbb{R}d, we define G as the orthogonal group leaving \mathcal{L} invariant. Starting from a basic kinetic model on G we construct a collision operator on \mathcal{L} which keeps all the essential features of the classical Boltzmann collision operator....
Article / Chapter
All rights reserved
2006-12-05

Approximations to the gelation phase of an aerosol

We investigate a time discretized version of the Smoluchowski coagulation equation. By means of a numerical example we prove its suitability as a basis for the efficient simulation of the transition to gelation.
Article / Chapter
All rights reserved
2005-09-01

Gelation of stochastic diffusion-coagulation systems

We investigate aerosol systems diffusing in space and study their gelation properties. In particular we work out the role of fluctuations which turn stable configurations into metastable ones, and the influence of randomly distributed sources and sinks.
Dissertation
2005-04-22

A hexagonal collision model for the numerical solution of the Boltzmann...

In kompakter Form werden die Hauptergebnisse der diskreten Boltzmann-Gleichung basierend auf hexagonalen Elementen vorgestellt. Zwecks Lösung dieses Problems mittels des hexagonalen diskreten Geschwindigkeitsmodells, werden im R^2 automatisch beliebig große Sechseckgitter generiert. Zur Identifikation...
Article / Chapter
All rights reserved
2004-12-06

Diffusion limits for discrete velocity models in a thin gap

We consider discrete kinetic models of a gas moving in a small gap with thickness h. Under an appropriate scaling of the variables, we introduce a formal series expansion to study the limit h --> 0. As a necessary condition for the validity of the expansion we derive a nonlinear diffusion equation.
Article / Chapter
OA NLZ
1999

On a Monte Carlo scheme for Smoluchowski's coagulation equation

We propose a Monte Carlo simulation scheme for the Smoluchowski equation of aerosol dynamics and discuss its numerical efficiency.
Berlin [u.a.]: de Gruyter, 1999