Development and Application of a Multirate Multistep AB Method to a Discontinuous Galerkin ...

155 Pages·2009·1.88 MB·English

Development and Application of a
Multirate Multistep AB Method to a
Discontinuous Galerkin Method based
Particle In Cell Scheme
Diploma Thesis (Diplomarbeit)
by
cand. aer. Andreas Stock
Institut fu¨r Aerodynamik und Gasdynamik
Universita¨t Stuttgart
and
Division of Applied Mathematics
Brown University
Providence, RI, USA
October 21, 2009
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Fu¨r Kristina, Thomas und Monika.
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Preface
This thesis would not have been possible without the support and help of many people.
At this point I would like to say thank you to those people.
SpecialthankstomysupervisorsProf. C.D.MunzandProf. J.S.Hesthavenforgiving
me the opportunity to prepare my thesis at Brown University.
A very special thanks goes to my tutor Andreas Kl¨ockner. This thesis is related to
a certain degree with Andreas Kl¨ockner’s work as a PhD student of Prof. Hesthaven.
Andreas Kl¨ockner provided the tools and the theoretical background that enabled me
to perform my work successfully. I have learnt a lot from him. A big part of this
thesis comes from the great support of Andreas. Besides the studies Andreas Kl¨ockner
supported me also in the daily problems that obviously occur during any stay abroad.
He made it much easier for me to get around in Providence and to have an effective and
great stay.
The thesis has been financial supported by Deutscher Akademische Austauschdienst
(DAAD) and the Erich Becker Stiftung.
Many thanks to my colleagues from the Applied Math Department at Brown
University. Especially I’d like to thank Dr. Akil Narayan who always helped me in
solving problems that occurred during my work. I’d also like to thank the very friendly
and helpful administrative staff from the Applied Math department.
Providence, RI, USA, October 2009
Andreas Stock
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INSTITUT FU¨R AERODYNAMIK
UND GASDYNAMIK
DIREKTOR:PROF.DR.-ING.EWALDKRÄMER
Universita¨tStuttgart
PROF.DR.CLAUS-DIETERMUNZ
Task
This thesis shall investigate the development and application of a multirate multistep
Adams-Bashforth method within a Particle-in-Cell scheme based on a nodal discontin-
uous Galerkin (DG) method. In the literature the development and application of a
multirate linear multistep method was describe by Gear and Wells [1]. Based on this
paper a multirate multistep Adams-Bashforth method will be derived and implemented
inanexistingDGcode[2]andPICcode[3]. ComputationsforasignificantPICtestcase
will compare the multirate timestepping method with a classic Runge-Kutta single-rate
timestepper.
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Statement of Originality
This thesis has been performed independently with support by my supervisors Prof.
C.D. Munz, Prof. J.S. Hesthaven and A. Kl¨ockner. It contains no material that has
been accepted for the award of a degree in this or any other university. To my best
knowledge and belief, this thesis contains no material previously published or written
by another person except where due reference is made in the text.
Providence, RI, USA, October 2009
cand. aer. Andreas Stock
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