• 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 ...
    • 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 ...
    • 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 ...
    • 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, ...
    • A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media 

      Radu, Adrian Florin; Nordbotten, Jan Martin; Pop, Iuliu Sorin; Kumar, Kundan (Peer reviewed; Journal article, 2015-12)
      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 ...
    • Two-phase flow in porous media: dynamic capillarity and heterogeneous media 

      van Duijn, Cornelius J.; Cao, Xiulei; Pop, Iuliu Sorin (Peer reviewed; Journal article, 2015-08-11)
      We investigate a two-phase porous media flow model, in which dynamic effects are taken into account in phase pressure difference. We consider a one-dimensional heterogeneous case, with two adjacent homogeneous blocks ...
    • An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube 

      Marban, David Landa; Bødtker, Gunhild; Kumar, Kundan; Pop, Iuliu Sorin; Radu, Adrian Florin (Peer reviewed; Journal article, 2020-01-21)
      In this paper, we derive upscaled equations for modeling biofilm growth in porous media. The resulting macroscale mathematical models consider permeable multi-species biofilm including water flow, transport, detachment and ...