| 1. |
- Both, Jakub Wiktor, et al.
(författare)
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Robust fixed stress splitting for Biot’s equations in heterogeneous media
- 2017
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Ingår i: Applied Mathematics Letters. - Amsterdam, Netherlands : Elsevier. - 0893-9659 .- 1873-5452. ; 68, s. 101-108
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Tidskriftsartikel (refereegranskat)abstract
- We study the iterative solution of coupled flow and geomechanics in heterogeneous porous media, modeled by a three-field formulation of the linearized Biot's equations. We propose and analyze a variant of the widely used Fixed Stress Splitting method applied to heterogeneous media. As spatial discretization, we employ linear Galerkin finite elements for mechanics and mixed finite elements (lowest order Raviart Thomas elements) for flow. Additionally, we use implicit Euler time discretization. The proposed scheme is shown to be globally convergent with optimal theoretical convergence rates. The convergence is rigorously shown in energy norms employing a new technique. Furthermore, numerical results demonstrate robust iteration counts with respect to the full range of Lame parameters for homogeneous and heterogeneous media. Being in accordance with the theoretical results, the iteration count is hardly influenced by the degree of heterogeneities.
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| 2. |
- Nissen, Anna, et al.
(författare)
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Heterogeneity preserving upscaling for heat transport in fractured geothermal reservoirs
- 2018
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Ingår i: Computational Geosciences. - : Springer. - 1420-0597 .- 1573-1499. ; 22:2, s. 451-467
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Tidskriftsartikel (refereegranskat)abstract
- In simulation of fluid injection in fractured geothermal reservoirs, the characteristics of the physical processes are severely affected by the local occurence of connected fractures. To resolve these structurally dominated processes, there is a need to develop discretization strategies that also limit computational effort. In this paper, we present an upscaling methodology for geothermal heat transport with fractures represented explicitly in the computational grid. The heat transport is modeled by an advection-conduction equation for the temperature, and solved on a highly irregular coarse grid that preserves the fracture heterogeneity. The upscaling is based on different strategies for the advective term and the conductive term. The coarse scale advective term is constructed from sums of fine scale fluxes, whereas the coarse scale conductive term is constructed based on numerically computed basis functions. The method naturally incorporates the coupling between solution variables in the matrix and in the fractures, respectively, via the discretization. In this way, explicit transfer terms that couple fracture and matrix solution variables are avoided. Numerical results show that the upscaling methodology performs well, in particular for large upscaling ratios, and that it is applicable also to highly complex fracture networks.
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| 3. |
- Radu, Florin Adrian, et al.
(författare)
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A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media
- 2015
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 289, s. 134-141
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Tidskriftsartikel (refereegranskat)abstract
- In this work we consider a mathematical model for two-phase flow in porous media. The fluids are assumed immiscible and incompressible and the solid matrix non-deformable. The mathematical model for the two-phase flow is written in terms of the global pressure and a complementary pressure (obtained by using the Kirchhoff transformation) as primary unknowns. For the spatial discretization, finite volumes have been used (more precisely the multi-point flux approximation method) and in time the backward Euler method has been employed. We present here a new linearization scheme for the nonlinear system arising after the temporal and spatial discretization. We show that the scheme is linearly convergent. Numerical experiments are presented that sustain the theoretical results.
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| 4. |
- Reveron, Manuel Antonio Borregales, et al.
(författare)
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Iterative solvers for Biot model under small and large deformations
- 2021
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Ingår i: Computational Geosciences. - : Springer. - 1420-0597 .- 1573-1499. ; 25, s. 687-699
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Tidskriftsartikel (refereegranskat)abstract
- We considerL-scheme and Newton-based solvers for Biot model under large deformation. The mechanical deformation follows the Saint Venant-Kirchoff constitutive law. Furthermore, the fluid compressibility is assumed to be non-linear. A Lagrangian frame of reference is used to keep track of the deformation. We perform an implicit discretization in time (backward Euler) and propose two linearization schemes for solving the non-linear problems appearing within each time step: Newton's method andL-scheme. Each linearization scheme is also presented in a monolithic and a splitting version, extending the undrained split methods to non-linear problems. The convergence of the solvers, here presented, is shown analytically for cases under small deformation and numerically for examples under large deformation. Illustrative numerical examples are presented to confirm the applicability of the schemes, in particular, for large deformation.
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| 5. |
- Vasilyev, Leonid, et al.
(författare)
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On the Properties of the Parameter Space of the Generalized Continuum Transport Model for Description of Fluid Flow in Porous Networks
- 2017
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Ingår i: Transport in Porous Media. - : Springer Science and Business Media LLC. - 0169-3913 .- 1573-1634. ; 119:3, s. 673-688
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Tidskriftsartikel (refereegranskat)abstract
- Generalized transport models, such as Dual and Multiple Continua Models, Global Random Walk, Multirate Mass Transfer and Continuous Time Random Walk are widely used for description of anomalous transport in fractured and porous media. For these models the form of the parameter space is crucial for the most accurate description of anomalous effects as well as the mean transport phenomenon. Constraining of the parameter space is required for the proper interpretation of the physical properties taking place. In this study the Generalized Continuum Transport model is considered as a versatile tool for the parameter space selection as well as better quantification of anomalous (non-Fickian) transport. Different variants of the parameter space are applied to the GCT model and the breakthrough curves obtained from the pore-network models with strong anomalities are fitted. Flexibility of the model is demonstrated through its static and dynamic adaptivity to network structure and transport complexity. The beneficial results of the curve fitting are also compared with the classical models. It is thus demonstrated that the complexity of the model as well as the model parameters can be directly determined based on fine-scale simulations.
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