Change search
Refine search result
1 - 31 of 31
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1.
    Almani, T.
    et al.
    UT Austin, Ctr Subsurface Modeling, ICES, Austin, TX 78712 USA.;Saudi Arabian Oil Co, Dhahran, Saudi Arabia..
    Kumar, Kundan
    Univ Bergen, Math Inst, N-5020 Bergen, Norway..
    Dogru, A.
    Saudi Arabian Oil Co, Dhahran, Saudi Arabia..
    Singh, G.
    UT Austin, Ctr Subsurface Modeling, ICES, Austin, TX 78712 USA..
    Wheeler, M. F.
    UT Austin, Ctr Subsurface Modeling, ICES, Austin, TX 78712 USA..
    Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics2016In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 311, p. 180-207Article in journal (Refereed)
    Abstract [en]

    We consider multirate iterative schemes for the Biot system modeling coupled flow and geomechanics in a poro-elastic medium. The multirate iterative coupling scheme exploits the different time scales for the mechanics and flow problems by taking multiple finer time steps for flow within one coarse mechanics time step. We adapt the fixed stress split algorithm that decouples the flow and mechanics equations for the multirate case and perform an iteration between the two problems until convergence. We provide a fully discrete scheme that uses Backward Euler time discretization and mixed spaces for flow and conformal Galerkin for mechanics. Our analysis is based on studying the equations satisfied by the difference of iterates and using Banach contraction argument to prove that the corresponding scheme is a fixed point contraction. The analysis provides the value of an adjustable coefficient used in the proposed iterative coupling algorithms. Furthermore, we show that the converged quantities satisfy the variational weak form for the coupled discrete system. (C) 2016 Elsevier B.V. All rights reserved.

  • 2.
    Almani, T.
    et al.
    Austin, USA.
    Kumar, Kundan
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). University of Bergen, Norway.
    Singh, G.
    Austin, USA.
    Wheeler, M. F.
    Austin, USA.
    Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium2019In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 78, no 8, p. 2682-2699Article in journal (Refereed)
    Abstract [en]

    We consider single rate and multirate explicit schemes for the Biot system modeling coupled flow and geomechanics in a poro-elastic medium. These schemes are widely used in practice that follows a sequential procedure in which the flow and mechanics problems are fully decoupled. In such a scheme, the flow problem is solved first with time-lagging the displacement term followed by the mechanics solve. The multirate explicit coupling scheme exploits the different time scales for the mechanics and flow problems by taking multiple finer time steps for flow within one coarse mechanics time step. We provide fully discrete schemes for both the single and multirate approaches that use Backward Euler time discretization and mixed spaces for flow and conformal Galerkin for mechanics. We perform a rigorous stability analysis and derive the conditions on reservoir parameters and the number of finer flow solves to ensure stability for both schemes. Furthermore, we investigate the computational time savings for explicit coupling schemes against iterative coupling schemes.

  • 3.
    Almani, T.
    et al.
    Center for Subsurface Modeling, ICES, UT-Austin, Austin, USA; Saudi Arabian Oil Company (Aramco), Dhahran, Saudi Arabia.
    Kumar, Kundan
    Mathematics Institute, University of Bergen, Bergen, Norway.
    Wheeler, M. F.
    Center for Subsurface Modeling, ICES, UT-Austin, Austin, USA.
    Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics2017In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 21, no 5-6, p. 1157-1172Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider an iterative coupling scheme for solving a fully discretized Biot system based on the fixed-stress split coupling algorithm. Specifically, we derive a priori error estimates for quantifying the error between the solution obtained at any iterate and the true solution. Our approach is based on studying the equations satisfied by the difference of iterates and utilizing a Banach contraction argument to show that the corresponding scheme is a fixed point iteration. Obtained contraction results are then used to derive theoretical convergence error estimates for the single rate iterative coupling scheme. We compare our numerical computations against the theoretically derived contraction estimates and show a good agreement with theory.

  • 4.
    Almani, T.
    et al.
    Saudi Arabian Oil Company (Aramco), Saudi Arabia.
    Manea, A.
    Saudi Arabian Oil Company (Aramco), Saudi Arabia.
    Kumar, Kundan
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). University of Bergen, Norway.
    Dogru, A. H.
    Saudi Arabian Oil Company (Aramco), Saudi Arabia; MIT, USA.
    Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media2019In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499Article in journal (Refereed)
    Abstract [en]

    Recently, an accurate coupling between subsurface flow and reservoir geomechanics has received more attention in both academia and industry. This stems from the fact that incorporating a geomechanics model into upstream flow simulation is critical for accurately predicting wellbore instabilities and hydraulic fracturing processes. One of the recently introduced iterative coupling algorithms to couple flow with geomechanics is the undrained split iterative coupling algorithm as reported by Kumar et al. (2016) and Mikelic and Wheeler (Comput. Geosci. 17: 455–461 2013). The convergence of this scheme is established in Mikelic and Wheeler (Comput. Geosci. 17:455–461 2013) for the single rate iterative coupling algorithm and in Kumar et al. (2016) for the multirate iterative coupling algorithm, in which the flow takes multiple finer time steps within one coarse mechanics time step. All previously established results study the convergence of the scheme in homogeneous poroelastic media. In this work, following the approach in Almani et al. (2017), we extend these results to the case of heterogeneous poroelastic media, in which each grid cell is associated with its own set of flow and mechanics parameters for both the single rate and multirate schemes. Second, following the approach in Almani et al. (Comput. Geosci. 21:1157–1172 2017), we establish a priori error estimates for the single rate case of the scheme in homogeneous poroelastic media. To the best of our knowledge, this is the first rigorous and complete mathematical analysis of the undrained split iterative coupling scheme in heterogeneous poroelastic media.

  • 5.
    Bogers, J.
    et al.
    TU Eindhoven, The Netherlands.
    Kumar, Kundan
    TU Eindhoven, The Netherlands.
    Notten, P. H. L.
    TU Eindhoven, The Netherlands.
    Oudenhoven, J. F. M.
    TU Eindhoven, The Netherlands.
    Pop, I. S.
    TU Eindhoven, The Netherlands.
    A multiscale domain decomposition approach for chemical vapor deposition2013In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 246, p. 65-73Article in journal (Refereed)
    Abstract [en]

    We consider the process of chemical vapor deposition on a trenched Si substrate. To understand the process (including e.g. the layer conformality) at the trench scale (microscale), we need solutions at both the trench and reactor scales (macroscale). Due to the huge difference in size of these scales, straightforward numerical computations are very challenging. To overcome this difficulty, we consider a multiscale approach by introducing an intermediate scale (the mesoscale). We start with a time-continuous model describing the transport processes and then perform time discretization. At each time step, using the ideas of domain decomposition inspired from Lions (1988) [4], we provide iterative coupling conditions for these three different scales. Using a weak formulation for the time-discrete equations, we prove the convergence of this iterative scheme at each time step. The approach also provides an alternative proof for the existence of the solutions for the time-discrete formulation. (C) 2012 Elsevier B.V. All rights reserved.

  • 6.
    Borregales, Manuel
    et al.
    University of Bergen, Norway..
    Radu, Florin A.
    University of Bergen, Norway..
    Kumar, Kundan
    University of Bergen, Norway.
    Nordbotten, Jan M.
    University of Bergen, Norway.; Princeton University, USA..
    Robust iterative schemes for non-linear poromechanics2018In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 22, no 4, p. 1021-1038Article in journal (Refereed)
    Abstract [en]

    We consider a non-linear extension of Biot's model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. Specifically, we study the case when the volumetric stress and the fluid density are non-linear functions satisfying certain assumptions. We perform an implicit discretization in time (backward Euler) and propose two iterative schemes for solving the non-linear problems appearing within each time step: a splitting algorithm extending the undrained split and fixed stress methods to non-linear problems, and a monolithic L-scheme. The convergence of both schemes are shown rigorously. Illustrative numerical examples are presented to confirm the applicability of the schemes and validate the theoretical results.

  • 7.
    Both, Jakub W.
    et al.
    Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway..
    Kumar, Kundan
    Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway..
    Nordbotten, Jan M.
    Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway.;Princeton Univ, Dept Civil & Environm Engn, E-208 E Quad, Princeton, NJ 08544 USA..
    Radu, Florin A.
    Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway..
    Iterative Methods for Coupled Flow and Geomechanics in Unsaturated Porous Media2017In: Poromechanics VI: Proceedings Of The Sixth Biot Conference On Poromechanics / [ed] Vandamme, M Dangla, P Pereira, JM Ghabezloo, S, American Society of Civil Engineers (ASCE), 2017, p. 411-418Conference paper (Refereed)
    Abstract [en]

    This work concerns the linearization of a three-field discretization of generalized Biot's equations describing coupled fluid flow and mechanical deformation in unsaturated porous media. The model of interest employs the effective stress based on the so-called equivalent pore pressure and can be interpreted as linear mechanics nonlinearly coupled with Richards' equation. As linearization, we apply simultaneously the L-scheme and the Fixed Stress Splitting scheme, which have been established and analyzed for Richards' equation and the linear Biot's equations, respectively. Numerical results demonstrate robustness and mesh independent convergence rates, whereas the popular, locally convergent Newton's method does not display robust convergence for the numerical examples we present.

  • 8.
    Both, Jakub Wiktor
    et al.
    University of Bergen, Bergen, Norway.
    Borregales, Manuel
    University of Bergen, Bergen, Norway.
    Nordbotten, Jan Martin
    University of Bergen, Bergen, Norway; Princeton University, Princeton, NJ, USA.
    Kumar, Kundan
    University of Bergen, Bergen, Norway.
    Radu, Florin Adrian
    University of Bergen, Bergen, Norway.
    Robust fixed stress splitting for Biot’s equations in heterogeneous media2017In: Applied Mathematics Letters, ISSN 0893-9659, E-ISSN 1873-5452, Vol. 68, p. 101-108Article in journal (Refereed)
    Abstract [en]

    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.

  • 9.
    Bringedal, Carina
    et al.
    Univ Bergen, Geophys Inst, POB 7803, N-5020 Bergen, Norway.;Univ Hasselt, Fac Sci, Campus Diepenbeek,Agoralaan Bldg D, BE-3590 Diepenbeek, Belgium..
    Kumar, Kundan
    Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway..
    Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow2017In: Transport in Porous Media, ISSN 0169-3913, E-ISSN 1573-1634, Vol. 120, no 3, p. 553-577Article in journal (Refereed)
    Abstract [en]

    For a non-isothermal reactive flow process, effective properties such as permeability and heat conductivity change as the underlying pore structure evolves. We investigate changes of the effective properties for a two-dimensional periodic porous medium as the grain geometry changes. We consider specific grain shapes and study the evolution by solving the cell problems numerically for an upscaled model derived in Bringedal et al. (Transp Porous Media 114(2):371-393, 2016. doi 10.1007/s11242-015-0530-9). In particular, we focus on the limit behavior near clogging. The effective heat conductivities are compared to common porosity-weighted volume averaging approximations, and we find that geometric averages perform better than arithmetic and harmonic for isotropic media, while the optimal choice for anisotropic media depends on the degree and direction of the anisotropy. An approximate analytical expression is found to perform well for the isotropic effective heat conductivity. The permeability is compared to some commonly used approaches focusing on the limiting behavior near clogging, where a fitted power law is found to behave reasonably well. The resulting macroscale equations are tested on a case where the geochemical reactions cause pore clogging and a corresponding change in the flow and transport behavior at Darcy scale. As pores clog the flow paths shift away, while heat conduction increases in regions with lower porosity.

  • 10.
    Endo Kokubun, M. A.
    et al.
    University of Bergen, Norway.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Radu, F. A.
    University of Bergen, Norway.
    Kumar, Kundan
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Pop, I. S.
    University of Hasselt, Belgium.
    Keilegavlen, E.
    University of Bergen, Norway.
    Spildo, K.
    University of Bergen, Norway.
    A pore-scale study of transport of inertial particles by water in porous media2019In: Chemical Engineering Science, ISSN 0009-2509, E-ISSN 1873-4405, Vol. 207, p. 397-409Article in journal (Refereed)
    Abstract [en]

    We study the transport of inertial particles in water flow in porous media. Our interest lies in understanding the accumulation of particles including the possibility of clogging. We propose that accumulation can be a result of hydrodynamic effects: the tortuous paths of the porous medium generate regions of dominating strain, which favour the accumulation of particles. Numerical simulations show that essentially two accumulation regimes are identified: for low and for high flow velocities. When particles accumulate at the entrance of a pore throat (high-velocity region), a clog is formed. This significantly modifies the flow, as the partial blockage of the pore causes a local redistribution of pressure, which diverts the upstream water flow into neighbouring pores. Moreover, we show that accumulation in high velocity regions occurs in heterogeneous media, but not in homogeneous media, where we refer to homogeneity with respect to the distribution of the pore throat diameters.

  • 11.
    Ganis, Benjamin
    et al.
    Univ Texas Austin, ICES, Austin, TX 78712 USA..
    Kumar, Kundan
    Univ Texas Austin, ICES, Austin, TX 78712 USA..
    Pencheva, Gergina
    Univ Texas Austin, ICES, Austin, TX 78712 USA..
    Wheeler, Mary F.
    Univ Texas Austin, ICES, Austin, TX 78712 USA..
    Yotov, Ivan
    Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA..
    A global Jacobian method for mortar discretizations of a fully implicit two-phase flow model2014In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 12, no 4, p. 1401-1423Article in journal (Refereed)
    Abstract [en]

    We consider a fully implicit formulation for two-phase flow in a porous medium with capillarity, gravity, and compressibility in three dimensions. The method is implicit in time and uses the multiscale mortar mixed finite element method for a spatial discretization in a nonoverlapping domain decomposition context. The interface conditions between subdomains are enforced in terms of Lagrange multiplier variables defined on a mortar space. The novel approach in this work is to linearize the coupled system of subdomain and mortar variables simultaneously to form a global Jacobian. This algorithm is shown to be more efficient and robust compared to previous algorithms that relied on two separate nested linearizations of subdomain and interface variables. We also examine various upwinding methods for accurate integration of phase mobility terms near subdomain interfaces. Numerical tests illustrate the computational benefits of this scheme.

  • 12.
    Girault, Vivette
    et al.
    Univ Paris 06, Sorbonne Univ, CNRS, UMR 7598,Lab Jacques Louis Lions, 4 Pl Jussieu, F-75005 Paris, France..
    Kumar, Kundan
    Univ Bergen, Math Inst, Realfagbygget, Allegaten 41, Bergen, Norway..
    Wheeler, Mary F.
    Univ Texas Austin, ICES, Ctr Subsurface Modeling, Austin, TX 78712 USA..
    Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium2016In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 20, no 5, p. 997-1011Article in journal (Refereed)
    Abstract [en]

    We consider an iterative scheme for solving a coupled geomechanics and flow problem in a fractured poroelastic medium. The fractures are treated as possibly non-planar interfaces. Our iterative scheme is an adaptation due to the presence of fractures of a classical fixed stress-splitting scheme. We prove that the iterative scheme is a contraction in an appropriate norm. Moreover, the solution converges to the unique weak solution of the coupled problem.

  • 13.
    Kumar, Kundan
    et al.
    Univ Bergen, Math Inst, Bergen, Norway..
    Almani, Tameem
    UT Austin, ICES, CSM, Austin, TX USA..
    Singh, Gurpreet
    UT Austin, ICES, CSM, Austin, TX USA..
    Wheeler, Mary F.
    UT Austin, ICES, CSM, Austin, TX USA..
    Multirate Undrained Splitting for Coupled Flow and Geomechanics in Porous Media2016In: NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS (ENUMATH 2015) / [ed] Karasozen, B Manguoglu, M TezerSezgin, M Goktepe, S Ugur, O, Springer Publishing Company, 2016, p. 431-440Conference paper (Refereed)
    Abstract [en]

    We consider a multirate iterative scheme for the quasi-static Biot equations modelling the coupled flow and geomechanics in a porous medium. The iterative scheme is based on undrained splitting where the flow and mechanics equations are decoupled with the mechanics solve followed by the pressure solve. The multirate scheme proposed here uses different time steps for the two equations, that is, uses q flow steps for each coarse mechanics step and may be interpreted as using a regularization parameter for the mechanics equation. We prove the convergence of the scheme and the proof reveals the appropriate regularization parameter and also the effect of the number of flow steps within coarse mechanics step on the convergence rate.

  • 14.
    Kumar, Kundan
    et al.
    University of Bergen, Norway..
    Neuss-Radu, Maria
    University Erlangen Nurnberg, Germany..
    Pop, Iuliu Sorin
    University of Bergen, Norway; Hasselt University, Belgium.
    Homogenization of a pore scale model for precipitation and dissolution in porous media2016In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 81, no 5, p. 877-897Article in journal (Refereed)
    Abstract [en]

    In this article, we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media. The starting point is the pore scale model in van Duijn & Pop (2004), which is a coupled system of evolution equations, involving a parabolic equation which models ion transport in the fluid phase of a periodic porous medium, coupled to an ordinary differential equations modelling dissolution and precipitation at the grains boundary. The main challenge is in dealing with the dissolution and precipitation rates, which involve a monotone but possibly discontinuous function. In order to pass to the limit in these rate functions at the boundary of the grains, we prove strong two-scale convergence for the concentrations at the microscopic boundary and use refined arguments in order to identify the form of the macroscopic dissolution rate, which is again a discontinuous function. The resulting upscaled model is consistent with the Darcy scale model proposed in Knabner et al. (1995).

  • 15.
    Kumar, Kundan
    et al.
    Technische Universiteit Eindhoven.
    Pisarenco, Maxim
    Technische Universiteit Eindhoven.
    Rudnaya, Maria
    Technische Universiteit Eindhoven.
    Savcenco, Valeriu
    Technische Universiteit Eindhoven.
    A note on analysis and numerics of algae growth2014In: Nonlinear Analysis, ISSN 1468-1218, Vol. 15, p. 392-403Article in journal (Refereed)
  • 16.
    Kumar, Kundan
    et al.
    University of Texas at Austin, Austin, USA.
    Pop, I. S.
    Eindhoven University of TechnologyEindhovenThe Netherlands; University of Bergen, Bergen, Norway.
    Radu, F. A.
    University of Bergen, Bergen, Norway.
    Convergence analysis for a conformal discretization of a model for precipitation and dissolution in porous media2014In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 127, no 4, p. 715-749Article in journal (Refereed)
    Abstract [en]

    In this paper we discuss the numerical analysis of an upscaled (core scale) model describing the transport, precipitation and dissolution of solutes in a porous medium. The particularity lies in the modeling of the reaction term, especially the dissolution term, which has a multivalued character. We consider the weak formulation for the upscaled equation and provide rigorous stability and convergence results for both the semi-discrete (time discretization) and the fully discrete schemes. In doing so, compactness arguments are employed.

  • 17. Kumar, Kundan
    et al.
    Pop, I. S.
    Radu, F. A.
    Convergence analysis of mixed numerical schemes for reactive flow in a porous medium2013In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 51, no 4, p. 2283-2308Article in journal (Refereed)
  • 18. Kumar, Kundan
    et al.
    Pop, I. S.
    Radu, F. A.
    Numerical analysis for an upscaled model for dissolution and precipitation in porous media2013In: Numerical mathematics and advanced applications 2011: Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 / [ed] Herausgeber: Cangiani, A., Davidchack, R.L., Georgoulis, E.H., Gorban, A.N., Levesley, J., Tretyakov, M.V, Springer Berlin/Heidelberg, 2013, p. 703-711Chapter in book (Other academic)
  • 19.
    Kumar, Kundan
    et al.
    Center for Subsurface Modeling, The Uni versity of Texas at Austin, USA.
    van Helvoort, M.
    Supply Chain Development, Jumbo Supermarkten B.V., The Netherlands.
    Pop, I. S.
    Department of Mathematics and Computer Sciences, Eindhoven University of Technology, The Netherlands & Institute of Mathematics, University of Bergen, Bergen, Norway.
    Rigorous upscaling of rough boundaries for reactive flows2014In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 94, no 7-8, p. 623-644Article in journal (Refereed)
    Abstract [en]

    We consider a mathematical model for reactive flow in a channel having a rough (periodically oscillating) boundary with both period and amplitude ε. The ions are being transported by the convection and diffusion processes. These ions can react at the rough boundaries and get attached to form the crystal (precipitation) and become immobile. The reverse process of dissolution is also possible. The model involves non‐linear and multi‐valued rates and is posed in a fixed geometry with rough boundaries. We provide a rigorous justification for the upscaling process in which we define an upscaled problem defined in a simpler domain with flat boundaries. To this aim, we use periodic unfolding techniques combined with translation estimates. Numerical experiments confirm the theoretical predictions and illustrate a practical application of this upscaling process.

  • 20.
    Kumar, Kundan
    et al.
    Eindhoven University of Technology, Netherlands.
    van Noorden, T. L.
    Eindhoven University of Technology, Netherlands.
    Pop, I. S.
    Eindhoven University of Technology, Netherlands.
    Effective dispersion equations for reactive flows involving free boundaries at the microscale2011In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 9, no 1, p. 29-58Article in journal (Refereed)
    Abstract [en]

    We consider a pore-scale model for reactive flow in a thin two-dimensional strip, where the convective transport dominates the diffusion. Reactions take place at the lateral boundaries of the strip (the walls), where the reaction product can deposit in a layer with a nonnegligible thickness compared to the width of the strip. This leads to a free boundary problem, in which the moving interface between the fluid and the deposited (solid) layer is explicitly taken into account. Using asymptotic expansion methods, we derive an upscaled, one-dimensional model by averaging in the transversal direction. The result is consistent with (Taylor dispersion) models obtained previously for a constant geometry. Finally, numerical computations are presented to compare the outcome of the effective (upscaled) model with the transversally averaged, two-dimensional solution.

  • 21. Kumar, Kundan
    et al.
    van Noorden, Tycho L.
    Wheeler, Mary F.
    Wick, Thomas
    An ALE-based method for reaction-induced boundary movement towards clogging2015In: Numerical mathematics and advanced applications—ENUMATH 2013: Proceedings of ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013 / [ed] Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M., Springer, 2015, Vol. 103, p. 633-641Chapter in book (Other academic)
  • 22.
    Kumar, Kundan
    et al.
    Tech Univ Eindhoven, CASA, NL-5600 MB Eindhoven, Netherlands..
    van Noorden, Tycho
    Dept Math, Chair Appl Math 1, D-91058 Erlangen, Germany..
    Pop, Iuliu Sorin
    Tech Univ Eindhoven, CASA, NL-5600 MB Eindhoven, Netherlands..
    Upscaling Of Reactive Flows In Domains With Moving Oscillating Boundaries2014In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 7, no 1, p. 95-111Article in journal (Refereed)
    Abstract [en]

    We consider the flow and transport of chemically reactive substances (precursors) in a channel over substrates having complex geometry. In particular, these substrates are in the form of trenches forming oscillating boundaries. The precursors react at the boundaries and get deposited. The deposited layers lead to changes in the geometry and are explicitly taken into account. Consequently, the system forms a free boundary problem. Using formal asymptotic techniques, we obtain the upscaled equations for the system where these equations are defined on a domain with flat boundaries. This provides a huge gain in computational time. Numerical experiments show the effectiveness of the upscaling process.

  • 23.
    Kumar, Kundan
    et al.
    Univ Texas Austin, Inst Computat Engn & Sci, Ctr Subsurface Modeling, Austin, TX 78712 USA..
    Wheeler, Mary F.
    Univ Texas Austin, Inst Computat Engn & Sci, Ctr Subsurface Modeling, Austin, TX 78712 USA..
    Wick, Thomas
    Univ Texas Austin, Inst Computat Engn & Sci, Ctr Subsurface Modeling, Austin, TX 78712 USA..
    Reactive Flow And Reaction-Induced Boundary Movement In A Thin Channel2013In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 35, no 6, p. B1235-B1266Article in journal (Refereed)
    Abstract [en]

    We study the reactive flow in a thin strip where the geometry changes take place due to reactions. Specifically, we consider precipitation-dissolution processes taking place at the lateral boundaries of the strip. The geometry changes depend on the concentration of the solute in the bulk (trace of the concentration), which makes the problem a free-moving boundary problem. The numerical computations are challenging in view of the nonlinearities in the description of the reaction rates. In addition to this, the movement of the boundary depends on the unknown concentration (and hence part of the solution), and the computation of the coupled model remains a delicate issue. Our aim is to develop appropriate numerical techniques for the computation of the solutions of the coupled convection-diffusion problem and the equation describing the geometry changes. The performance is demonstrated with the help of several numerical tests.

  • 24.
    Pop, Iuliu Sorin
    et al.
    Hasselt Univ, Fac Sci, Campus Diepenbeek,Agoralaan Gebouw D, BE-3590 Diepenbeek, Belgium.;Univ Bergen, Dept Math, Postboks 7803, N-5020 Bergen, Norway..
    Bogers, Jeroen
    ASML Netherlands BV, Run 6501, NL-5504 DR Veldhoven, Netherlands..
    Kumar, Kundan
    Univ Bergen, Dept Math, Postboks 7803, N-5020 Bergen, Norway..
    Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition2017In: Vietnam Journal of Mathematics, ISSN 2305-221X, E-ISSN 2305-2228, Vol. 45, no 1-2, p. 77-102Article in journal (Refereed)
    Abstract [en]

    We consider a reactive transport model in a fractured porous medium. The particularity appears in the conditions imposed at the interface separating the block and the fracture, which involves a nonlinear transmission condition. Assuming that the fracture has thickness epsilon, we analyze the resulting problem and prove the convergence toward a reduced model in the limit epsilon a dagger y0. The result is a model defined on an interface (the reduced fracture) and acting as a boundary condition for the equations defined in the block. Using both formal and rigorous arguments, we obtain the reduced models for different flow regimes, expressed through a moderate or a high P,clet number.

  • 25.
    Radu, Florin A.
    et al.
    University of Bergen, Norway.
    Kumar, Kundan
    University of Bergen, Norway.
    Nordbotten, Jan M.
    University of Bergen, Norway.
    Pop, Iuliu S.
    University of Bergen, Norway; Hasselt University, Belgium.
    A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities2018In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, Vol. 38, no 2, p. 884-920Article in journal (Refereed)
  • 26.
    Radu, Florin Adrian
    et al.
    Univ Bergen, Dept Math, N-5020 Bergen, Norway..
    Nordbotten, Jan Martin
    Univ Bergen, Dept Math, N-5020 Bergen, Norway..
    Pop, Iuliu Sorin
    Univ Bergen, Dept Math, N-5020 Bergen, Norway.;Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands..
    Kumar, Kundan
    Univ Bergen, Dept Math, N-5020 Bergen, Norway.;Univ Texas Austin, ICES, Austin, TX 78712 USA..
    A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media2015In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 289, p. 134-141Article in journal (Refereed)
    Abstract [en]

    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.

  • 27.
    Salama, Amgad
    et al.
    Univ Regina, Regina, SK, Canada..
    El Amin, Mohamed F.
    Effat Univ, Jeddah, Saudi Arabia..
    Kumar, Kundan
    Univ Bergen, Bergen, Norway..
    Sun, Shuyu
    King Abdullah Univ Sci & Technol, Thuwal, Saudi Arabia..
    Flow and transport in tight and shale formations: A review2017In: Geofluids, ISSN 1468-8115, E-ISSN 1468-8123, article id UNSP 4251209Article, review/survey (Refereed)
    Abstract [en]

    A review on the recent advances of the flow and transport phenomena in tight and shale formations is presented in this work. Exploration of oil and gas in resources that were once considered inaccessible opened the door to highlight interesting phenomena that require attention and understanding. The length scales associated with transport phenomena in tight and shale formations are rich. From nanoscale phenomena to field-scale applications, a unified frame that is able to encounter the varieties of phenomena associated with each scale may not be possible. Each scale has its own tools and limitations that may not, probably, be suitable at other scales. Multiscale algorithms that effectively couple simulations among various scales of porous media are therefore important. In this article, a review of the different length scales and the tools associated with each scale is introduced. Highlights on the different phenomena pertinent to each scale are summarized. Furthermore, the governing equations describing flow and transport phenomena at different scales are investigated. In addition, methods to solve these equations using numerical techniques are introduced. Cross-scale analysis and derivation of linear and nonlinear Darcy's scale laws from pore-scale governing equations are described. Phenomena occurring at molecular scales and their thermodynamics are discussed. Flow slippage at the nanosize pores and its upscaling to Darcy's scale are highlighted. Pore network models are discussed as a viable tool to estimate macroscopic parameters that are otherwise difficult to measure. Then, the environmental aspects associated with the different technologies used in stimulating the gas stored in tight and shale formations are briefly discussed.

  • 28.
    Salama, Amgad
    et al.
    Univ Regina, Regina, SK, Canada..
    Sun, Shuyu
    King Abdullah Univ Sci & Technol, Jeddah, Saudi Arabia..
    El Amin, Mohamed F.
    Effat Univ, Jeddah, Saudi Arabia..
    Wang, Yi
    Univ Petr, Beijing Key Lab Urban Oil & Gas Distribut Technol, MOE Key Lab Petr Engn, Natl Engn Lab Pipeline Safety, Beijing 102249, Peoples R China..
    Kumar, Kundan
    Univ Bergen, Bergen, Norway..
    Flow and Transport in Porous Media: A Multiscale Focus2017In: Geofluids, ISSN 1468-8115, E-ISSN 1468-8123, article id UNSP 7579015Article in journal (Other academic)
  • 29.
    Sepasian, Neda
    et al.
    Eindhoven University of Technology, Netherlands.
    Kumar, Kundan
    University of Bergen, Norway.
    Breeuwer, Marcel
    Eindhoven University of Technology, Netherlands.
    A geometrical approach to find corresponding patches in 3D medical surfaces2015In: Similarity-based pattern recognition: Third international workshop, SIMBAD 2015 / [ed] Feragen, A., Pelillo, M. & Loog, M., Springer, 2015, p. 217-219Conference paper (Refereed)
  • 30.
    Storvik, E.
    et al.
    University Bergen Norway.
    Both, J. W.
    University Bergen Norway.
    Kumar, Kundan
    University Bergen Norway.
    Nordbotten, J. M.
    University Bergen Norway.
    Radu, F. A.
    University Bergen Norway.
    On the optimization of the fixed-stress splitting for Biot’s equations2019In: International Journal for Numerical Methods in EngineeringArticle in journal (Refereed)
    Abstract [en]

    In this work, we are interested in efficiently solving the quasi-static, linear Biot model for poroelasticity. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot’s equations. It is well known that the convergence properties of the method strongly depend on the applied stabilization/tuning parameter. We show theoretically that, in addition to depending on the mechanical properties of the porous medium and the coupling coefficient, they also depend on the fluid flow and spatial discretization properties. The type of analysis presented in this paper is not restricted to a particular spatial discretization, although it is required to be inf-sup stable with respect to the displacement-pressure formulation. Furthermore, we propose a way to optimize this parameter that relies on the mesh independence of the scheme’s optimal stabilization parameter. Illustrative numerical examples show that using the optimized stabilization parameter can significantly reduce the number of iterations. © 2019 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd.

  • 31.
    Vasilyev, Leonid
    et al.
    Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway..
    Nordbotten, Jan Martin
    Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway..
    Radu, Adrian Florin
    Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway..
    Kumar, Kundan
    Univ Bergen, Dept Math, POB 7803, N-5020 Bergen, Norway..
    On the Properties of the Parameter Space of the Generalized Continuum Transport Model for Description of Fluid Flow in Porous Networks2017In: Transport in Porous Media, ISSN 0169-3913, E-ISSN 1573-1634, Vol. 119, no 3, p. 673-688Article in journal (Refereed)
    Abstract [en]

    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.

1 - 31 of 31
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf