• Ecological and evolutionary dynamics of interconnectedness and modularity 

      Nordbotten, Jan Martin; Levin, Simon A.; Szathmáry, Eörs; Stenseth, Nils Christian (Peer reviewed; Journal article, 2018-01-23)
      In this contribution, we develop a theoretical framework for linking microprocesses (i.e., population dynamics and evolution through natural selection) with macrophenomena (such as interconnectedness and modularity within ...
    • Effective Preconditioners for Mixed-Dimensional Scalar Elliptic Problems 

      Hu, Xiaozhe; Keilegavlen, Eirik; Nordbotten, Jan Martin (Journal article; Peer reviewed, 2023)
      Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for ...
    • An efficient software framework for performing industrial risk assessment of leakage for geological storage of CO2 

      Dobossy, Mark E.; Celia, Michael A.; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2011)
      In response to anthropogenic CO2 emissions, geological storage has emerged as a practical and scalable bridge technology while renewables and other environmentally friendly energy production methods mature. While an ...
    • Efficient water table evolution discretization using domain transformation 

      Boon, Wietse; Balbarini, Nicola; Binning, Philip John; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2017-02)
      Domain transformation methods are useful techniques for solving problems on non-stationary domains. In this work, we consider the evolution of the water table in an unconfined aquifer. This nonlinear, time-dependent problem ...
    • Field-case simulation of CO2-plume migration using vertical-equilibrium models 

      Nilsen, Halvor Møll; Herrera, Paulo; Ashraf, Seyed Meisam; Ligaard, Ingeborg S.; Iding, Martin; Hermanrud, Christian; Lie, Knut-Andreas; Nordbotten, Jan Martin; Dahle, Helge K.; Keilegavlen, Eirik (Peer reviewed; Journal article, 2011)
      When injected in deep saline aquifers, CO2 moves radially away from the injection well and progressively higher in the formation because of buoyancy forces. Analyzes have shown that after the injection period, CO2 will ...
    • Finite volume discretization for poroelastic media with fractures modeled by contact mechanics 

      Berge, Runar Lie; Berre, Inga; Keilegavlen, Eirik; Nordbotten, Jan Martin; Wohlmuth, Barbara (Peer reviewed; Journal article, 2020)
      A fractured poroelastic body is considered where the opening of the fractures is governed by a nonpenetration law, whereas slip is described by a Coulomb‐type friction law. This physical model results in a nonlinear ...
    • Finite volume hydromechanical simulation in porous media 

      Nordbotten, Jan Martin (Peer reviewed; Journal article, 2014-05-27)
      Cell-centered finite volume methods are prevailing in numerical simulation of flow in porous media. However, due to the lack of cell-centered finite volume methods for mechanics, coupled flow and deformation is usually ...
    • Finite volume methods for elasticity with weak symmetry 

      Keilegavlen, Eirik; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2017-11)
      We introduce a new cell‐centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor. The method is motivated by the need for robust discretization methods for deformation and ...
    • A Finite-Volume-Based Module for Unsaturated Poroelasticity 

      Varela, Jhabriel; Gasda, Sarah Eileen; Keilegavlen, Eirik; Nordbotten, Jan Martin (Chapter, 2021)
      In this chapter, we present fv-unsat, a multipoint finite-volume–based solver for unsaturated flow in deformable and nondeformable porous media. The latter is described using the mixed form of Richards’ equation, whereas ...
    • The Fixed-Stress splitting scheme for Biot's equations as a modified Richardson iteration: Implications for optimal convergence 

      Storvik, Erlend; Both, Jakub; Nordbotten, Jan Martin; Radu, Florin Adrian (Journal article; Peer reviewed, 2021)
      The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanics subproblems while adding a stabilizing term to the flow equation, which ...
    • The FluidFlower Validation Benchmark Study for the Storage of CO2 

      Flemisch, Bernd; Nordbotten, Jan Martin; Fernø, Martin; Juanes, Ruben; Both, Jakub Wiktor; Class, Holger; Delshad, Mojdeh; Doster, Florian; Ennis-King, Jonathan; Franc, Jacques; Geiger, Sebastian; Gläser, Dennis; Green, Christopher; Gunning, James; Hajibeygi, Hadi; Jackson, Samuel J.; Jammoul, Mohamad; Karra, Satish; Li, Jiawei; Matthäi, Stephan K.; Miller, Terry; Shao, Qi; Spurin, Catherine; Stauffer, Philip; Tchelepi, Hamdi; Tian, Xiaoming; Viswanathan, Hari; Voskov, Denis; Wang, Yuhang; Wapperom, Michiel; Wheeler, Mary F.; Wilkins, Andrew; Youssef, AbdAllah A.; Zhang, Ziliang (Journal article; Peer reviewed, 2023)
      Successful deployment of geological carbon storage (GCS) requires an extensive use of reservoir simulators for screening, ranking and optimization of storage sites. However, the time scales of GCS are such that no sufficient ...
    • Fractal structures in freezing brine 

      Alyaev, Sergey; Keilegavlen, Eirik; Nordbotten, Jan Martin; Pop, Iuliu Sorin (Peer reviewed; Journal article, 2017-09)
      The process of initial ice formation in brine is a highly complex problem. In this paper, we propose a mathematical model that captures the dynamics of nucleation and development of ice inclusions in brine. The primary ...
    • Functional analysis and exterior calculus on mixed-dimensional geometries 

      Boon, Wietse; Nordbotten, Jan Martin; Vatne, Jon Eivind (Journal article; Peer reviewed, 2020-07-12)
      We are interested in differential forms on mixed-dimensional geometries, in the sense of a domain containing sets of d-dimensional manifolds, structured hierarchically so that each d-dimensional manifold is contained in ...
    • Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem 

      Kumar, Kundan; Kyas, Svetlana; Nordbotten, Jan Martin; Repin, Sergey (Journal article; Peer reviewed, 2021)
      The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing ...
    • High-accuracy phase-field models for brittle fracture based on a new family of degradation functions 

      Sargado, Juan Michael; Keilegavlen, Eirik; Berre, Inga; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2018-02)
      Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture ...
    • The impact of local-scale processes on large-scale CO2 migration and immobilization 

      Gasda, Sarah Eileen; Nordbotten, Jan Martin; Celia, Michael A. (Peer reviewed; Journal article, 2011)
      Storage security of injected carbon dioxide (CO2) is an essential component of risk management for geological carbon sequestration operations. During the injection and early post-injection periods, CO2 leakage may occur ...
    • Inexact linear solvers for control volume discretizations in porous media 

      Keilegavlen, Eirik; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2014-12-03)
      We discuss the construction ofmulti-level inexact linear solvers for control volume discretizations for porous media. The methodology forms a contrast to standard iterative solvers by utilizing an algebraic hierarchy of ...
    • Influence of natural convection in a porous medium when producing from borehole heat exchangers 

      Bringedal, Carina; Berre, Inga; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2013-08)
      Convection currents in a porous medium form when the medium is subject to sufficient heating from below (or equivalently, cooling from above) or when cooled or heated from the side. In the context of geothermal energy ...
    • Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations 

      Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin; Pop, Iuliu Sorin; Radu, Florin Adrian (Peer reviewed; Journal article, 2019)
      Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical ...
    • Iterative solvers for Biot model under small and large deformation 

      Borregales Reveron, Manuel Antonio; Kumar, Kundan; Nordbotten, Jan Martin; Radu, Florin Adrian (Journal article; Peer reviewed, 2021)
      We consider L-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 ...