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Burbulla, Samuel

Samuel Burbulla

M. Sc.

Research assistant
Institute of Applied Analysis and Numerical Simulation
Chair of Applied Mathematics

Contact

+49 711 685 65395
Email

Pfaffenwaldring 57
70569 Stuttgart
Deutschland
Room: 7.126

Publications

2023
1. S. Burbulla, M. Hörl, and C. Rohde, “Flow in Porous Media with Fractures of Varying Aperture,” SIAM J. Sci. Comput, vol. 45, no. 4, Art. no. 4, 2023, doi: 10.1137/22M1510406.
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  BibTeX
  @article{burbulla2022flow, abstract = {We study single-phase flow in a fractured porous medium at a macroscopic scale that allows to model fractures individually. The flow is governed by Darcy's law in both fractures and porous matrix. We derive a new mixed-dimensional model, where fractures are represented by $(n-1)$-dimensional interfaces between $n$-dimensional subdomains for $n\ge 2$. In particular, we suggest a generalization of the model in~[22] by accounting for asymmetric fractures with spatially varying aperture. Thus, the new model is particularly convenient for the description of surface roughness or for modeling curvilinear or winding fractures. The wellposedness of the new model is proven under appropriate conditions. Further, we formulate a discontinuous Galerkin discretization of the new model and validate the model by performing two- and three-dimensional numerical experiments.}, author = {Burbulla, Samuel and Hörl, Maximilian and Rohde, Christian}, doi = {10.1137/22M1510406}, eprint = {https://doi.org/10.1137/22M1510406}, journal = {SIAM J. Sci. Comput}, number = 4, pages = {A1519-A1544}, title = {Flow in Porous Media with Fractures of Varying Aperture}, url = {https://doi.org/10.1137/22M1510406}, volume = 45, year = 2023 }
  Link
  https://doi.org/10.1137/22M1510406
2. S. Burbulla, L. Formaggia, C. Rohde, and A. Scotti, “Modeling fracture propagation in poro-elastic media combining phase-field and discrete fracture models,” Comput. Methods Appl. Mech. Engrg., vol. 403, 2023, doi: https://doi.org/10.1016/j.cma.2022.115699.
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  @article{rohde2023modeling, abstract = {We present a novel model for fluid-driven fracture propagation in poro-elastic media. Our approach combines ideas from dimensionally reduced discrete fracture models with diffuse phase-field models. The main advantage of this combined approach is that the fracture geometry is always represented explicitly, while the propagation remains geometrically flexible. We prove that our model is thermodynamically consistent. In order to solve our model numerically, we propose a mixed-dimensional discontinuous Galerkin scheme with a computational grid fully conforming to the fractures. As the fracture propagates, the diffuse phase-field acts as indicator to identify new fracture facets to be added to the discrete fracture network. Numerical experiments demonstrate that our approach reproduces classical scenarios for fracturing porous media}, author = {Burbulla, Samuel and Formaggia, Luca and Rohde, Christian and Scotti, Anna}, doi = {https://doi.org/10.1016/j.cma.2022.115699}, issn = {0045-7825}, journal = {Comput. Methods Appl. Mech. Engrg.}, title = {Modeling fracture propagation in poro-elastic media combining phase-field and discrete fracture models}, url = {https://www.sciencedirect.com/science/article/pii/S0045782522006545}, volume = 403, year = 2023 }
  Link
  https://www.sciencedirect.com/science/article/pii/S0045782522006545
2022
1. S. Burbulla, A. Dedner, M. Hörl, and C. Rohde, “Dune-MMesh: The Dune Grid Module for Moving Interfaces,” J. Open Source Softw., vol. 7, no. 74, Art. no. 74, 2022, doi: 10.21105/joss.03959.
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  @article{Burbulla2022, author = {Burbulla, Samuel and Dedner, Andreas and Hörl, Maximilian and Rohde, Christian}, doi = {10.21105/joss.03959}, journal = {J. Open Source Softw.}, number = 74, pages = 3959, publisher = {The Open Journal}, title = {Dune-MMesh: The Dune Grid Module for Moving Interfaces}, url = {https://doi.org/10.21105/joss.03959}, volume = 7, year = 2022 }
  Link
  https://doi.org/10.21105/joss.03959
2. S. Burbulla and C. Rohde, “A finite-volume moving-mesh method for two-phase flow in fracturing porous media,” J. Comput. Phys., p. 111031, 2022, doi: https://doi.org/10.1016/j.jcp.2022.111031.
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  @article{burbulla2022finitevolume, abstract = {Multiphase flow in fractured porous media can be described by discrete fracture matrix models that represent the fractures as dimensionally reduced manifolds embedded in the bulk porous medium. Generalizing earlier work on this approach we focus on immiscible two-phase flow in time-dependent fracture geometries, i.e., the fracture itself and the aperture of the fractures might evolve in time. For dynamic fracture geometries of that kind, neglecting capillary forces, we deduce by transversal averaging of a full dimensional description a dimensionally reduced model that governs the geometric evolution and the flow dynamics. The core computational contribution is a mixed-dimensional finite-volume discretization based on a conforming moving-mesh ansatz. This finite-volume moving-mesh (FVMM) algorithm is tracking the fractures' motions as a family of unions of facets of the mesh. Notably, the method permits arbitrary movement of facets of the triangulation while keeping the mass conservation constraint. In a series of numerical examples we investigate the modeling error of the reduced model as it compares to the original full dimensional model. Moreover, we show the performance of the finite-volume moving-mesh algorithm for the complex wave pattern that is induced by the interaction of saturation fronts and evolving fractures.}, author = {Burbulla, Samuel and Rohde, Christian}, doi = {https://doi.org/10.1016/j.jcp.2022.111031}, journal = {J. Comput. Phys.}, pages = 111031, title = {A finite-volume moving-mesh method for two-phase flow in fracturing porous media}, url = {https://www.sciencedirect.com/science/article/pii/S0021999122000936}, year = 2022 }
  Link
  https://www.sciencedirect.com/science/article/pii/S0021999122000936
2020
1. S. Burbulla and C. Rohde, “A fully conforming finite volume approach to two-phase flow in fractured porous media,” in Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, R. Klöfkorn, E. Keilegavlen, F. A. Radu, and J. Fuhrmann, Eds., in Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. Cham: Springer International Publishing, 2020, pp. 547–555. doi: https://doi.org/10.1007/978-3-030-43651-3_51.
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  @inproceedings{Burbulla2020, abstract = {In many natural and technical applications in porous media fluid's flow behavior is highly affected by fractures. Many approaches employ mixed-dimensional models that model thin features as dimension-reduced manifolds. Following this idea, we consider porous media where dominant heterogeneities are geometrically represented by sharp interfaces. We model incompressible two-phase flow in porous media both in the bulk porous medium and within the fractures. We present a reliable and geometrically flexible implementation of a fully conforming finite volume approach within the DUNE framework for two and three spatial dimensions. The implementation is based on the new dune-mmesh grid implementation that manages bulk and surface triangulation simultaneously. The model and the implementation are extended to handle fracture junctions. We apply our scheme to benchmark cases with complex fracture networks to show the reliability of the approach.}, address = {Cham}, author = {Burbulla, Samuel and Rohde, Christian}, booktitle = {Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples}, doi = {https://doi.org/10.1007/978-3-030-43651-3_51}, editor = {Klöfkorn, Robert and Keilegavlen, Eirik and Radu, Florin A. and Fuhrmann, Jürgen}, pages = {547-555}, publisher = {Springer International Publishing}, title = {A fully conforming finite volume approach to two-phase flow in fractured porous media}, url = {https://link.springer.com/chapter/10.1007%2F978-3-030-43651-3_51}, year = 2020 }
  Link
  https://link.springer.com/chapter/10.1007%2F978-3-030-43651-3_51
2. I. Berre et al., “Verification benchmarks for single-phase flow in three-dimensional fractured porous media.” 2020.
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  @misc{berre2020verification, archiveprefix = {arXiv}, author = {Berre, Inga and Boon, Wietse M. and Flemisch, Bernd and Fumagalli, Alessio and Gläser, Dennis and Keilegavlen, Eirik and Scotti, Anna and Stefansson, Ivar and Tatomir, Alexandru and Brenner, Konstantin and Burbulla, Samuel and Devloo, Philippe and Duran, Omar and Favino, Marco and Hennicker, Julian and Lee, I-Hsien and Lipnikov, Konstantin and Masson, Roland and Mosthaf, Klaus and Nestola, Maria Giuseppina Chiara and Ni, Chuen-Fa and Nikitin, Kirill and Schädle, Philipp and Svyatskiy, Daniil and Yanbarisov, Ruslan and Zulian, Patrick}, eprint = {2002.07005}, primaryclass = {math.NA}, title = {Verification benchmarks for single-phase flow in three-dimensional fractured porous media}, year = 2020 }
3. T. Koch et al., “DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling,” Computers & Mathematics with Applications, 2020, doi: https://doi.org/10.1016/j.camwa.2020.02.012.
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  @article{KOCH2020, abstract = {We present version 3 of the open-source simulator for flow and transport processes in porous media DuMux. DuMux is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMux, version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.}, author = {Koch, Timo and Gläser, Dennis and Weishaupt, Kilian and Ackermann, Sina and Beck, Martin and Becker, Beatrix and Burbulla, Samuel and Class, Holger and Coltman, Edward and Emmert, Simon and Fetzer, Thomas and Grüninger, Christoph and Heck, Katharina and Hommel, Johannes and Kurz, Theresa and Lipp, Melanie and Mohammadi, Farid and Scherrer, Samuel and Schneider, Martin and Seitz, Gabriele and Stadler, Leopold and Utz, Martin and Weinhardt, Felix and Flemisch, Bernd}, doi = {https://doi.org/10.1016/j.camwa.2020.02.012}, issn = {0898-1221}, journal = {Computers & Mathematics with Applications}, title = {DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling}, url = {http://www.sciencedirect.com/science/article/pii/S0898122120300791}, year = 2020 }
  Link
  http://www.sciencedirect.com/science/article/pii/S0898122120300791
4. J. T. Gerstenberger, S. Burbulla, and D. Kröner, “Discontinuous Galerkin method for incompressible two-phase flows,” Submitted to: Springer Proceedings in Mathematics & Statistics, 2020.
  - BibTeX
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  @article{Gerstenberger2020, author = {Gerstenberger, Janick Thomas and Burbulla, Samuel and Kröner, Dietmar}, journal = {Submitted to: Springer Proceedings in Mathematics & Statistics}, title = {Discontinuous Galerkin method for incompressible two-phase flows}, year = 2020 }

Vita

Since 2018	Doctoral Researcher at the Institute of Applied Analysis and Numerical Simulation, University of Stuttgart Advisor: Prof. Dr. Christian Rohde
2016 - 2018	Master of Science in Mathematics, University of Freiburg Thesis: "Transport einer Zweiphasenströmung mit einer scharfen Grenzschicht in drei Dimensionen." Supervisor: Prof. Dr. Dietmar Kröner
2016 - 2018	Graduate Assistant at the Institute of Mathematics, Departement of Applied Mathematics, University of Freiburg
2012 - 2016	Bachelor of Science in Mathematics, University of Freiburg, Germany

Project participant in Collaborative Research Centre (SFB) 1313 "Interface-Driven Multi-Field Processes in Porous Media – Flow, Transport and Deformation'', German Research Foundation (DFG), Project B03 "Heterogeneous multi-scale methods for two-phase flow in dynamically fracturing porous media", 2018-2021.

Software

Dune-MMesh (https://dune-mmesh.readthedocs.io)

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Samuel Burbulla

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2023

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2022

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2020

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