thesis.aux 8.07 KB
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\relax 
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\providecommand\hyper@newdestlabel[2]{}
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\abx@aux@refcontext{none/global//global/global}
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\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
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\@writefile{toc}{\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax }
\@writefile{lof}{\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax }
\@writefile{lot}{\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax }
\abx@aux@cite{MEYER2021103936}
\abx@aux@segm{0}{0}{MEYER2021103936}
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\abx@aux@cite{MEYER2021101592}
\abx@aux@segm{0}{0}{MEYER2021101592}
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\abx@aux@cite{petsc-web-page}
\abx@aux@segm{0}{0}{petsc-web-page}
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\abx@aux@cite{MEYER2021103936}
\abx@aux@segm{0}{0}{MEYER2021103936}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {2}Parallel Flow Solver}{2}{section.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}PETSc Interface}{2}{subsection.2.1}\protected@file@percent }
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\abx@aux@cite{hypre-web-page}
\abx@aux@segm{0}{0}{hypre-web-page}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Solver}{3}{subsection.2.2}\protected@file@percent }
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Limitations}{3}{subsection.2.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Results}{3}{subsection.2.4}\protected@file@percent }
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\abx@aux@cite{MEYER2021101592}
\abx@aux@segm{0}{0}{MEYER2021101592}
\abx@aux@cite{MEYER2021103936}
\abx@aux@segm{0}{0}{MEYER2021103936}
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\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Pressures $p_{\mathrm  {in}}$ and $p_{\mathrm  {out}}$ are applied to in-pores and out-pores respectively, driving the network flow. The resulting pressure system is solved with the available solvers and the different fluxes are shown for the individual pores in the case of PETSc (using 4 processes). Since the sequential solvers produce an identical plot, they are omitted here. \relax }}{4}{figure.caption.1}\protected@file@percent }
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\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
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\newlabel{fig:balance}{{1}{4}{Pressures $p_{\mathrm {in}}$ and $p_{\mathrm {out}}$ are applied to in-pores and out-pores respectively, driving the network flow. The resulting pressure system is solved with the available solvers and the different fluxes are shown for the individual pores in the case of PETSc (using 4 processes). Since the sequential solvers produce an identical plot, they are omitted here. \relax }{figure.caption.1}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {3}Parallel Network Generation}{4}{section.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Cell Lists}{4}{subsection.3.1}\protected@file@percent }
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\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Cell lists visualized in 2D. The neighborhood of the pore highlighted in red is marked in blue. Because the cell-size is the maximally permissible throat length $L_m$, only the pores contained within the blue region must be considered during neighbor search. Finally, the periodic buffer layers, containing copies of pores on the opposite side from the interior, are painted in orange.\relax }}{5}{figure.caption.2}\protected@file@percent }
\newlabel{fig:cell}{{2}{5}{Cell lists visualized in 2D. The neighborhood of the pore highlighted in red is marked in blue. Because the cell-size is the maximally permissible throat length $L_m$, only the pores contained within the blue region must be considered during neighbor search. Finally, the periodic buffer layers, containing copies of pores on the opposite side from the interior, are painted in orange.\relax }{figure.caption.2}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Iterative Algorithm}{5}{subsection.3.2}\protected@file@percent }
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Results}{6}{subsection.3.3}\protected@file@percent }
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\@writefile{loa}{\defcounter {refsection}{0}\relax }\@writefile{loa}{\contentsline {algorithm}{\numberline {1}{\ignorespaces Connect pores in parallel\relax }}{6}{algorithm.1}\protected@file@percent }
\newlabel{alg:connect}{{1}{6}{Connect pores in parallel\relax }{algorithm.1}{}}
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\@writefile{lot}{\defcounter {refsection}{0}\relax }\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Sample run of parallel pore-connecting algorithm using 4 threads. The generated network is 3 times as large as the base network in all directions. The maximal feasible number of throats is 103464, of which 27 were not realized due to there being no possible candidates left for these remaining pores.\relax }}{7}{table.caption.3}\protected@file@percent }
\newlabel{table:iter}{{1}{7}{Sample run of parallel pore-connecting algorithm using 4 threads. The generated network is 3 times as large as the base network in all directions. The maximal feasible number of throats is 103464, of which 27 were not realized due to there being no possible candidates left for these remaining pores.\relax }{table.caption.3}{}}
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\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {A}PETSc Installation}{7}{appendix.A}\protected@file@percent }
\newlabel{appendix:install}{{A}{7}{PETSc Installation}{appendix.A}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {B}Base Network}{7}{appendix.B}\protected@file@percent }
\newlabel{appendix:base}{{B}{7}{Base Network}{appendix.B}{}}
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\abx@aux@refcontextdefaultsdone
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\abx@aux@defaultrefcontext{0}{MEYER2021103936}{none/global//global/global}
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\abx@aux@defaultrefcontext{0}{MEYER2021101592}{none/global//global/global}
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\abx@aux@defaultrefcontext{0}{petsc-web-page}{none/global//global/global}
\abx@aux@defaultrefcontext{0}{hypre-web-page}{none/global//global/global}
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\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Network consisting of 2636 pores and 4291 throats, inscribed within a cube extending $1.07\cdot 10^{-3}$m in each spatial direction. The pore-arrangement is obviously \emph  {not uniform}, as can be seen by the clustering of pores in some regions, while others are mostly undisturbed. The \emph  {porosity}, measured as the relative fraction of volume taken up by the void-space geometry, is roughly $32\%$.\relax }}{8}{figure.caption.4}\protected@file@percent }
\newlabel{fig:base}{{3}{8}{Network consisting of 2636 pores and 4291 throats, inscribed within a cube extending $1.07\cdot 10^{-3}$m in each spatial direction. The pore-arrangement is obviously \emph {not uniform}, as can be seen by the clustering of pores in some regions, while others are mostly undisturbed. The \emph {porosity}, measured as the relative fraction of volume taken up by the void-space geometry, is roughly $32\%$.\relax }{figure.caption.4}{}}