• 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 ...
    • Higher order space-time elements for a non-linear Biot model 

      Borregales Reveron, Manuel Antonio; Radu, Florin Adrian (Lecture Notes in Computational Science and Engineering ; 126, Conference object; Peer reviewed; Book, 2019)
      In this work, we consider a non-linear extension of the linear, quasi-static Biot’s model. Precisely, we assume that the volumetric strain and the fluid compressibility are non-linear functions. We propose a fully discrete ...
    • Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations 

      Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin; Pop, Iuliu Sorin; Radu, Florin Adrian (Conference object; 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 schemes for surfactant transport in porous media 

      Illiano, Davide; Pop, Iuliu Sorin; Radu, Florin Adrian (Journal article; Peer reviewed, 2020)
      In this work, we consider the transport of a surfactant in variably saturated porous media. The water flow is modelled by the Richards equations and it is fully coupled with the transport equation for the surfactant. Three ...
    • 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, 2020-07-18)
      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 ...
    • Mathematics and Medicine: How mathematics, modelling and simulations can lead to better diagnosis and treatments 

      Hanson, Erik Andreas; Hodneland, Erlend; Lorentzen, Rolf Johan; Nævdal, Geir; Nordbotten, Jan Martin; Sævareid, Ove; Zanna, Antonella (Lecture Notes in Computational Science and Engineering, Chapter; Peer reviewed; Journal article, 2019)
      Starting with the discovery of X-rays by Röntgen in 1895, the progress in medical imaging has been extraordinary and immensely beneficial to diagnosis and therapy. Parallel to the increase of imaging accuracy, there is the ...
    • Microfluidic study of effects of flow velocity and nutrient concentration on biofilm accumulation and adhesive strength in the flowing and no-flowing microchannels 

      Liu, Na; Skauge, Tormod; Landa-Marbán, David; Hovland, Beate; Thorbjørnsen, Bente; Radu, Florin Adrian; Vik, Bartek Florczyk; Baumann, Thomas; Bødtker, Gunhild (Journal article; Peer reviewed, 2019)
      Biofilm accumulation in porous media can cause pore plugging and change many of the physical properties of porous media. Engineering bioplugging may have significant applications for many industrial processes, while improved ...
    • On the optimization of the fixed‐stress splitting for Biot's equations 

      Storvik, Erlend; Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin; Radu, Florin Adrian (Peer reviewed; Journal article, 2019)
      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. ...
    • A pore-scale model for permeable biofilm: Numerical simulations and laboratory experiments 

      Landa-Marban, David; Liu, Na; Pop, Iuliu Sorin; Kumar, Kundan; Pettersson, Per; Bødtker, Gunhild; Skauge, Tormod; Radu, Florin Adrian (Peer reviewed; Journal article, 2019)
      In this paper, we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided into two phases: water and biofilm. The biofilm is assumed to consist of four components: water, ...
    • Robust iterative schemes for non-linear poromechanics 

      Borregales Reveron, Manuel Antonio; Radu, Florin Adrian; Kumar, Kundan; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2018)
      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 ...
    • Transport of polymer particles in oil–water flow in porous media: Enhancing oil recovery 

      Endo Kokubun, Max Akira; Radu, Florin Adrian; Keilegavlen, Eirik; Kumar, Kundan; Spildo, Kristine (Peer reviewed; Journal article, 2019)
      We study a heuristic, core-scale model for the transport of polymer particles in a two-phase (oil and water) porous medium. We are motivated by recent experimental observations which report increased oil recovery when ...
    • 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 ...
    • Well-posedness of the fully coupled quasi-static thermo-poroelastic equations with nonlinear convective transport 

      Brun, Mats Kirkesæther; Radu, Florin Adrian; Ahmed, Elyes; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2019-03)
      This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's ...