Mathematical analysis of macroscopic models for slow dense granular flow [Elektronische Ressource] / Aleksander Grm

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• Mathematics

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• Publié par: technische_universitat_kaiserslautern
• Publié le: 01 janvier 2007
• Nombre de lectures: 41
• Langue: English
• Poids de l'ouvrage: 1 Mo

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Mathematical Analysis of Macroscopic Models
for Slow Dense Granular Flow
Aleksander GRM
April 2007
Department of Mathematics
Univeristy of KaiserslauternMathematical Analysis of Macroscopic Models
for Slow Dense Granular Flow
Aleksander GRM
Vom Fachbereich Mathematik
der Technischen Universit¨at Kaiserslautern
zur Verleihung des akademischen Grades
Doktor der Naturwissenschaften
(Doctor rerum naturalium, Dr. rer. nat.)
genehmigte Dissertation
1. Gutacher: Prof. Dr. Axel Klar
2. Gutacher: Prof. Dr. Dr. h.c. em. Helmut Neunzert
Tag der Disputation: 26.04.2007
D 386Abstract
In this dissertation we present analysis of macroscopic models for slow dense
granular flow. Models are derived from plasticity theory with yield condition
and flow rule. Corner stone equations are conservation of mass and conservation
of momentum with special constitutive law. Such models are considered in the
class of generalised Newtonian fluids, where viscosity depends on the pressure
and modulo of the strain-rate tensor. We showed the hyperbolic nature for the
evolutionary model in 1D and ill-posed behaviour for 2D and 3D. The steady
state equations are always hyperbolic. In the 2D problem we derived a prototype
nonlinear backward parabolic equation for the velocity and the similar equation
fortheshear-rate. AnalysisofderivedPDEshowedthefiniteblowuptime. Blow
up time depends on the initial condition. Full 2D and antiplane 3D model were
investigated numerically with finite element method. For 2D model we showed
the presence of boundary layers. Antiplane 3D model was investigated with the
Runge Kutta Discontinuous Galerkin method with mesh addoption. Numerical
results confirmed that such a numerical method can be a good choice for the
simulations of the slow dense granular flow.To my wife ...Acknowledgements
IwishtoexpressmydeepestappreciationtomysupervisorProf. AxelKlarforhis
support,guidanceandencouragement. IamhighlyindebtedtoProf. em. Helmut
Neunzert for giving me the opportunity of doing my Ph.D. in Kaiserslautern and
guiding me in the first year.
I am very grateful to Dr. Raimund Wegener for being human department boss.
I am particularly indebted to Dr. Robert Feßler for the useful hints, advises and
introducing me into the topic of granular flow. I would like to thank the group
”Transportforgang¨ e” at Fraunhofer ITWM especially Satyananda Panda, Nicole
Marheineke, Jevgenij Jegorovs, Sergiy Pereverzyev, Mathieu Sellier for providing
friendly working atmosphere and Alfonso Caiazzo for being a good friend.
The financial support from Franuhofer ITWM, Department of Transport Pro-
cesses is gratefully acknowledged. Without their support, present work would
not have been possible.
Finally, my special thanks go to my wife and my family in particular for their
love, support and encouragement.