• Auxiliary variables for 3D multiscale simulations in heterogeneous porous media 

      Sandvin, Andreas; Keilegavlen, Eirik; Nordbotten, Jan Martin (Journal article, 2013-04-01)
      The multiscale control-volume methods for solving problems involving flow in porous media have gained much interest during the last decade. Recasting these methods in an algebraic framework allows one to consider them as ...
    • Consistency issues in pdf methods 

      Suciu, Nicolae; Schüler, Lennart; Radu, Adrian Florin; Attinger, Sabine; Vamo̧s, Cǎlin; Knabner, Peter (Peer reviewed; Journal article, 2015)
      Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations for the one-point one-time PDF are usually ...
    • A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media 

      Radu, Florin Adrian; Kumar, Kundan; Nordbotten, Jan Martin; Pop, Sorin Iuliu (Research report, 2017)
      In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic ...
    • 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 ...
    • Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids 

      Sandvin, Andreas; Nordbotten, Jan Martin; Aavatsmark, Ivar (Peer reviewed; Journal article, 2011-06)
      Multiscale methods can in many cases be viewed as special types of domain decomposition preconditioners. The localisation approximations introduced within the multiscale framework are dependent upon both the heterogeneity ...
    • Solute transport in aquifers with evolving scale heterogeneity 

      Suciu, Nicolae; Attinger, Sabine; Radu, Adrian Florin; Vamo̧s, Cǎlin; Vanderborght, Jan; Vereecken, Harry; Knabner, Peter (Peer reviewed; Journal article, 2015)
      Transport processes in groundwater systems with spatially heterogeneous properties often exhibit anomalous behavior. Using first-order approximations in velocity fluctuations we show that anomalous superdiffusive behavior ...
    • Stable cell-centered finite volume discretization for biot equations 

      Nordbotten, Jan Martin (Peer reviewed; Journal article, 2016-03-29)
      In this paper we discuss a new discretization for the Biot equations. The discretization treats the coupled system of deformation and flow directly, as opposed to combining discretizations for the two separate subproblems. ...
    • A unified multilevel framework of upscaling and domain decomposition 

      Sandvin, Andreas; Nordbotten, Jan Martin; Aavatsmark, Ivar (Conference object, 2010)
      We consider multiscale preconditioners for a class of mass-conservative domain-decomposition (MCDD) methods. For the application of reservoir simulation, we need to solve large linear systems, arising from finite-volume ...
    • Upscaling of the Coupling of Hydromechanical and Thermal Processes in a Quasi-static Poroelastic Medium 

      Brun, Mats Kirkesæther; Berre, Inga; Nordbotten, Jan Martin; Radu, Florin Adrian (Peer reviewed; Journal article, 2018-08)
      We undertake a formal derivation of a linear poro-thermo-elastic system within the framework of quasi-static deformation. This work is based upon the well-known derivation of the quasi-static poroelastic equations (also ...