Publications
You can find all of my articles on my Google Scholar profile.
Selected Papers
SIAM Journal on Scientific Computing, 2023
We study single-phase flow in a fractured porous medium at a macroscopic scale that allows us to model fractures individually. The flow is governed by Darcy’s law in both fractures and a porous matrix. We derive a new mixed-dimensional model, where fractures are represented by (n-1)-dimensional interfaces between n-dimensional subdomains for n>=2. In particular, we suggest a generalization of the model in [V. Martin, J. Jaffré, and J. E. Roberts, SIAM J. Sci. Comput., 26 (2005), pp. 1667–1691] 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.
Citation: Samuel Burbulla, Maximilian Hörl, Christian Rohde (2023). Flow in porous media with fractures of varying aperture. SIAM Journal on Scientific Computing 45(4), A1519-A1544. https://epubs.siam.org/doi/abs/10.1137/22M1510406
Computer Methods in Applied Mechanics and Engineering, 2023
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.
Citation: Samuel Burbulla, Luca Formaggia, Christian Rohde, Anna Scotti (2023). Modeling fracture propagation in poro-elastic media combining phase-field and discrete fracture models. Computer Methods in Applied Mechanics and Engineering, Volume 403, Part A, 115699. https://www.sciencedirect.com/science/article/abs/pii/S0045782522006545
Journal of Computational Physics, 2022
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.
Citation: Samuel Burbulla, Christian Rohde (2022). A finite-volume moving-mesh method for two-phase flow in dynamically fracturing porous media. Journal of Computational Physics, Volume 458, 2022, 111031. https://www.sciencedirect.com/science/article/abs/pii/S0021999122000936
