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Updated thesis

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@article{MEYER2021103936,
title = {Random generation of irregular natural flow or pore networks},
journal = {Advances in Water Resources},
volume = {152},
pages = {103936},
year = {2021},
issn = {0309-1708},
doi = {https://doi.org/10.1016/j.advwatres.2021.103936},
url = {https://www.sciencedirect.com/science/article/pii/S0309170821000919},
author = {Daniel W. Meyer},
keywords = {Dendrogram, Clustering, Networks, Generator, Connectivity, Heterogeneity},
abstract = {Over the past years, tomographic scanning techniques like micro-CT have become popular for the acquisition of high-fidelity void-space geometries of natural porous media (e.g., Bultreys et al., 2016; Raeini et al., 2017). Limitations both in computing time and memory prohibit, however, direct numerical simulations of flow and transport in large resp. detailed sample geometries. Flow or pore networks derived from scans alleviate this limitation, but still necessitate a methodology to extrapolate to larger samples. In this work, we present a network generation algorithm that is particularly suited for heterogeneous irregular networks. While emulating from an existing base network new networks of equal or larger sizes, the outlined algorithm scales approximately linearly with the network node or pore count and maintains (1) node connectivity resp. pore coordination-number statistics, (2) geometrical pore/throat properties, as well as (3) the potentially inhomogeneous spatial clustering of pores. While existing methods address the first two properties, the third point is crucial especially in heterogeneous media to match flow/transport properties like the permeability that have a strong dependence on the spatial distance between connected pores. Moreover, the cubical networks generated by our algorithm are periodic in all spatial directions, thus eliminating topological boundary effects, which are not present in natural media. Bounded networks of arbitrary sizes can then be recovered by cutting the generated networks and thus flow/transport processes at larger scales can be studied while incorporating physically-based descriptions of pore-scale processes.}
}
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@misc{petsc-web-page,
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and Peter Brune and Kris Buschelman and Emil~M. Constantinescu and Lisandro Dalcin and Alp Dener
and Victor Eijkhout and William~D. Gropp and V\'{a}clav Hapla and Tobin Isaac and Pierre Jolivet
and Dmitry Karpeev and Dinesh Kaushik and Matthew~G. Knepley and Fande Kong and Scott Kruger
and Dave~A. May and Lois Curfman McInnes and Richard Tran Mills and Lawrence Mitchell and Todd Munson
and Jose~E. Roman and Karl Rupp and Patrick Sanan and Jason Sarich and Barry~F. Smith
and Stefano Zampini and Hong Zhang and Hong Zhang and Junchao Zhang},
title = {{PETS}c {W}eb page},
url = {https://petsc.org/},
howpublished = {\url{https://petsc.org/}},
year = {2021}
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@techreport{petsc-user-ref,
author = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Steven Benson and Jed Brown
and Peter Brune and Kris Buschelman and Emil Constantinescu and Lisandro Dalcin and Alp Dener
and Victor Eijkhout and William~D. Gropp and V\'{a}clav Hapla and Tobin Isaac and Pierre Jolivet
and Dmitry Karpeev and Dinesh Kaushik and Matthew~G. Knepley and Fande Kong and Scott Kruger
and Dave~A. May and Lois Curfman McInnes and Richard Tran Mills and Lawrence Mitchell and Todd Munson
and Jose~E. Roman and Karl Rupp and Patrick Sanan and Jason Sarich and Barry~F. Smith
and Stefano Zampini and Hong Zhang and Hong Zhang and Junchao Zhang},
title = {{PETSc/TAO} Users Manual},
institution = {Argonne National Laboratory},
number = {ANL-21/39 - Revision 3.16},
year = {2021}
}
@inproceedings{petsc-efficient,
author = {Satish Balay and William~D. Gropp and Lois Curfman McInnes and Barry~F. Smith},
title = {Efficient Management of Parallelism in Object Oriented Numerical Software Libraries},
booktitle = {Modern Software Tools in Scientific Computing},
editor = {E. Arge and A.~M. Bruaset and H.~P. Langtangen},
publisher = {Birkh{\"{a}}user Press},
pages = {163--202},
year = {1997}
}
thesis/thesis.aux
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\field{abstract}{Over the past years, tomographic scanning techniques like micro-CT have become popular for the acquisition of high-fidelity void-space geometries of natural porous media (e.g., Bultreys et al., 2016; Raeini et al., 2017). Limitations both in computing time and memory prohibit, however, direct numerical simulations of flow and transport in large resp. detailed sample geometries. Flow or pore networks derived from scans alleviate this limitation, but still necessitate a methodology to extrapolate to larger samples. In this work, we present a network generation algorithm that is particularly suited for heterogeneous irregular networks. While emulating from an existing base network new networks of equal or larger sizes, the outlined algorithm scales approximately linearly with the network node or pore count and maintains (1) node connectivity resp. pore coordination-number statistics, (2) geometrical pore/throat properties, as well as (3) the potentially inhomogeneous spatial clustering of pores. While existing methods address the first two properties, the third point is crucial especially in heterogeneous media to match flow/transport properties like the permeability that have a strong dependence on the spatial distance between connected pores. Moreover, the cubical networks generated by our algorithm are periodic in all spatial directions, thus eliminating topological boundary effects, which are not present in natural media. Bounded networks of arbitrary sizes can then be recovered by cutting the generated networks and thus flow/transport processes at larger scales can be studied while incorporating physically-based descriptions of pore-scale processes.}
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