Pore-scale direct numerical simulation of flow and transport in porous media [Elektronische Ressource] / vorgelegt von Sreejith Pulloor Kuttanikkad

Sujets

• Mathematics
• Physik

Informations

• Publié par: ruprecht-karls-universitat_heidelberg
• Publié le: 01 janvier 2009
• Nombre de lectures: 23
• Langue: Deutsch
• Poids de l'ouvrage: 13 Mo

Extrait

INAUGURAL - DISSERTATION
zur
ErlangungderDoktorwürde
der
Naturwissenschaftlich-MathematischenGesamtfakultät
der
Ruprecht-Karls-Universität
Heidelberg
vorgelegtvon
Sreejith Pulloor Kuttanikkad, M.S.
ausElankur(Kerala),Indien
TagdermündlichenPrüfung: 15.10.2009Pore-Scale Direct Numerical Simulation of
Flow and Transport in Porous Media
Gutachter: Prof. Dr. Peter Bastian
Prof. Dr. Kurt RothTo my extended family ...
especially to my parents, my grandparents, my
brother, my sister and to my wife!Porenskalige direkte numerische Simulation von Strmung und Transport in porsen
Medien
Diese Dissertation stellt Untersuchungen zur porenskaligen Simulation von Strömung
und Transport in porösen Medien vor und beschreibt die Anwendung eines neuen nu-
merischen Ansatzes zu porenskaliger Modellierung, basierend auf unstetigen Galerkin
(DG) Finiten Elementen. In diesem Ansatz werden die partiellen Differentialgleichun-
gen, die die Strömung auf der Porenskala bestimmen, direkt auf einer strukturierten
Partitionierung des Rechengebiets gelöst. Der Hauptvorteil ist, dass auf das Erstellen
einer konformen Triangulierung verzichtet werden kann. AuSSerdem ist dieser Ansatz
lokal massenerhaltend, eine wünschenswerte Eigenschaft für Transportsimulationen.
Dies erlaubt die effizientere Untersuchung von Prozessen auf der Porenskala und ihrem
Einfluss auf makroskopische Phänomene. Es wurde die Stokes-Strömung in zwei- und
dreidimensionalen undgeordneten Kugelpackungen berechnet und in einem random-
walk Teilchenverfolgungsmodell zur Simulation von Transport durch die Kugelpackung
benutzt. Die Permeabilitäten wurden berechnet und das asymptotische Dispersionsver-
halten des gelösten Stoffes für einen weiten Bereich der Péclet-Zahl untersucht. Die
Ergebnisse der Simulationen stimmen gut mit den Literaturdaten überein, was zeigt,
dass der hier gewählte Ansatz gut für porenskalige Simulation geeignet ist.
Pore-Scale Direct Numerical Simulation of Flow and Transport in Porous Media
This dissertation presents research on the pore-scale simulation of flow and transport in
porous media and describes the application of a new numerical approach based on the
discontinuous Galerkin (DG) finite elements to pore-scale modelling. In this approach,
the partial differential equations governing the flow at the pore-scale are solved directly
where the main advantage is that it does not require a body fitted grid and works
on a structured partition of the domain. Furthermore this approach is locally mass
conservative, a desirable property for transport simulation. This allows the investigation
of pore-scale processes and their effect on macroscopic behaviour more efficiently. The
Stokes flow in two and three dimensional disordered packing was solved and the flow
field was used in a random-walk particle tracking model to simulate the transport
through the packing. The permeabilities were computed and asymptotic behaviour of
solute dispersion for a wide range of Péclet numbers was studied. The simulated results
agree well with the data reported in the literature, which indicates that the approach
chosen here is well suited for pore-scale simulation.
ZusammenfassungAbstractAcknowledgements
I would like to express my profound gratitude to my advisers Prof. Dr. Peter Bastian
and Prof. Dr. Kurt Roth for the research opportunity that they provided me. I am
grateful to them for suggesting this interesting topic and for their continuous guidance,
support and keen interest in the progress of my work. I shall always cherish the
academic freedom that I have enjoyed under their guidance. Their scientific knowledge
and directions helped me to make this work possible.
I am most thankful to Dr. Olaf Ippisch and my colleagues Christian Engwer and
Markus Blatt for their constant help and many fruitful discussions and I appreciate their
scientific ideas. In particular, I am indebted to Christian for his work on UDG and for his
programming efforts. I have learnt a lot from them and would like to show my deep
respect for them. I extend my thanks to Thimo Neubaur for helping me during the initial
stages of my research and to Jö and Felix for always being helpful.
I gratefully acknowledge the scholarship offered by the International Graduiertenkol-
leg IGK 710 Complex Processes: Modeling, Simulation and Optimization at the Interdisci-
plinary Center of Scientific Computing (IWR). I am grateful for the opportunities that
the program offered and giving me a platform for the exchange of scientific knowledge.
Many thanks to my colleagues in the soil physics group and in IPVS Stuttgart: Dan,
Sven, Ute, Holger, Dr. H.-J. Vogel, Klaus, Stefan, Fereidoun, Enkaledja and all my former
and current colleagues for their support and friendliness.
Thanks are also to all DUNE developers for their excellent work, which helped me to
develop the required simulation codes using DUNE.
Special thanks to my wife Manisha for her love, support, encouragement and under-
standing. I am grateful for her consistent support during some difficult times.
I shall always recall with great fondness many of my friends: Nixon, Pradeep, Jishy,
Vinod, Shahi, Smitha, Lakshmi, Alex, Pauly, Beena, Badri, Adarsh, Prem, Ganesh. Thanks
also to Sabine for her nice hospitality during my stay in Heidelberg.
I would also like to thank many other people not listed who made my last few years a
memorable time of my life. Thank you, one and all.
Last but not least, I thank the God for always being with me and my parents, brother,
my wife and other family members for their love, support and constant encouragement.
You all have always been there for me, for that I am eternally grateful.
Sreejith Pulloor Kuttanikkad