### Updated plots and introduction of thesis

parent 1b5b3163
 ... ... @@ -13,20 +13,27 @@ comm = MPI.COMM_WORLD rank = comm.Get_rank() root = 0 def aggregate_flux(p, Q): def plot_flux(inpores, outpores, p, Q, solver_name): Qb = netflow.flux_balance(p, Q) flux_mean = 0.; flux_max = 0. # Compute flux balance statistics for _, balance in Qb.items(): flux_current = abs(balance) if flux_current > flux_max: flux_max = flux_current flux_mean += flux_current flux_mean /= len(Qb) # Exclude in- and out-pores respectively Qb = {pore: Qb[pore] for pore in Qb if (pore not in inpores) and (pore not in outpores)} x = np.arange(len(Qb)) Qp = np.array( [Qb[k] for k in Qb] ) Qm = np.array( [Qb[k] for k in Qb] ) Qs = np.array( [Qb[k] for k in Qb] ) return (flux_mean, flux_max) plt.figure() plt.title(r"Pore Flux Statistics for Solver: {}".format(solver_name)) plt.xlabel(r"Pore Index (no in-/out-pores)") plt.ylabel(r"Flux [$m^3s^{-1}$]") plt.plot(x, Qp, label=r"out-going") plt.plot(x, Qm, label=r"in-coming") plt.plot(x, Qs, label=r"sum") plt.legend() plt.savefig("../thesis/plots/flux_{}.png".format(solver_name)) plt.close() def main(): basenet = None ... ... @@ -47,8 +54,6 @@ def main(): len(outpores))) # Compute solution for each solver and compare flux balances mean_fluxes = {} max_fluxes = {} for solver in netflow.Solver: start = MPI.Wtime() p, Q = netflow.solve_flow_inout(network=basenet, pin=1e4, \ ... ... @@ -59,26 +64,8 @@ def main(): if rank == root: print("Solver: %s Time: %e s" % (solver.name, end - start)) flux_mean, flux_max = aggregate_flux(p, Q) mean_fluxes[solver.name] = flux_mean max_fluxes[solver.name] = flux_max # Post-processing on root only if (rank == root): labels = list(mean_fluxes.keys()) colors = ['b', 'r', 'g', 'orange'] heights = list(mean_fluxes.values()) x = np.arange(len(mean_fluxes)) plt.figure() plt.title(r"Comparison of Flux Balance Statistics of Solvers") plt.xlabel(r"Solver employed") plt.ylabel(r"Mean total pore flux in $[m^3s^{-1}]$") plt.bar(x, heights, tick_label=labels, color=colors) plt.show() plt.close() plot_flux(inpores, outpores, p, Q, solver.name) comm.Barrier() if __name__ == '__main__': main() main()

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 ... ... @@ -14,11 +14,11 @@ \@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}\protected@file@percent } \@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {2}Parallel Flow Solver}{2}\protected@file@percent } \@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}PETSc Interface}{2}\protected@file@percent } \@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Solver}{2}\protected@file@percent } \@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Results}{2}\protected@file@percent } \@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Solver}{3}\protected@file@percent } \@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Results}{3}\protected@file@percent } \@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 respective solvers from above and the mean total pore flux is shown in each case. With PETSc using 4 processes to solve the system. (AMG = algebraic multi-grid, CG = conjugate gradients, ILU = incomplete LU-preconditioning + GMRES)}}{3}\protected@file@percent } \newlabel{fig:balance}{{1}{3}} \abx@aux@refcontextdefaultsdone \abx@aux@defaultrefcontext{0}{MEYER2021103936}{none/global//global/global} \abx@aux@defaultrefcontext{0}{petsc-web-page}{none/global//global/global} \abx@aux@defaultrefcontext{0}{hypre-web-page}{none/global//global/global} \@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 respective solvers from above and the mean total pore flux is shown in each case. With PETSc using 4 processes to solve the system. (AMG = algebraic multi-grid, CG = conjugate gradients, ILU = incomplete LU-preconditioning + GMRES)}}{3}\protected@file@percent } \newlabel{fig:balance}{{1}{3}}
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 ... ... @@ -42,7 +42,7 @@ \vspace{5ex} \begin{multicols}{2} \section{Introduction} \hspace{0.5cm}The paper from \cite{MEYER2021103936} outlines a procedure for generating random realizations of larger flow networks, taking an existing base network, obtained from a scan of a porous medium, as input. Said network consists of spherical pores that are connected by cylindrical throats. The \emph{netflow} package that implements the algorithm from above also provides functionality for solving and analyzing the flow through such networks. The former of which is now to be parallelized in a distributed fashion so that it may support larger networks with up to 100 millions of pores. \hspace{0.5cm}Porous media are abundant in nature. Various types of soils harbor intricate networks that enable the flow of groundwater and subsequently the transport of important chemical compounds through the soil. To understand these natural phenomena, it is of key interest to study the flow through pore networks. However, this requires sufficiently large void-space geometries taken from porous bodies, which despite advances in scanning technologies, is infeasible. Additionally, in pursuit of simulation efficiency, the 3D images obtained from scans are converted into a simplified representation consisting of spherical pores (nodes), connected by cylindrical throats (edges). To overcome above size limitation, the paper from \cite{MEYER2021103936} outlines a procedure for generating random realizations of much larger flow networks, taking an existing base network, obtained from a scan of a porous medium, as input. Furthermore, this method is particularly useful for generating heterogeneous networks, characterized by irregular pore distributions. This is done with dendrogram-based clustering of pores in the original network, followed by random rotations of said clusters. When performed repeatedly and arranged in a 3-dimensional grid of perturbed base network copies, the resulting network, carrying over pore statistics such as coordination number \& radius, preserves the irregular pore structure of the original network. The \emph{netflow} package that implements the mentioned algorithm also provides functionality for solving and analyzing the flow through such networks. The former of which is now to be parallelized in a distributed fashion, so that it may support larger networks with up to 100 millions of pores. In a further step, the network generation algorithm shall be complemented by a parallel shared memory approach, specifically for connecting the generated pores in the resulting network. This is done directly in Python using the \verb|multiprocessing| library. \section{Parallel Flow Solver} \subsection{PETSc Interface} ... ... @@ -53,16 +53,16 @@ \hspace{0.5cm}In order to assess the quality of the pressure-solution obtained by this solver, we study the fluxes induced by the pore pressures for a given base network comprised of 2636 pores. In particular, we look at the sum of all in- and out-going fluxes per pore, obtained from the function \verb|flux_balance()|, and aggregated over all pores of the network. As expected from the conservation of mass, the mean is close to $0$ ($\approx 10^{-10}$) and the maximum is $\approx 10^{-7}$, which is in complete agreement with existing single-core solvers implemented in \emph{netflow}, see Figure ~\ref{fig:balance}. \end{multicols} \newpage \begin{figure}[h] \centering \includegraphics[width=0.8\textwidth]{plots/flux_balance.png} \includegraphics[width=0.8\textwidth]{plots/flux_PETSC.png} \caption{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 respective solvers from above and the mean total pore flux is shown in each case. With PETSc using 4 processes to solve the system. (AMG = algebraic multi-grid, CG = conjugate gradients, ILU = incomplete LU-preconditioning + GMRES)} \label{fig:balance} \end{figure} \newpage \centering \printbibliography \end{document} \ No newline at end of file
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