• Efficient Solvers for Nonstandard Models for Flow and Transport in Unsaturated Porous Media 

      Illiano, Davide; Both, Jakub Wiktor; Pop, Iuliu Sorin; Radu, Florin Adrian (Journal article; Peer reviewed, 2022)
      We study several iterative methods for fully coupled flow and reactive transport in porous media. The resulting mathematical model is a coupled, nonlinear evolution system. The flow model component builds on the Richards ...
    • 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 ...
    • Fronts in two-phase porous media flow problems: The effects of hysteresis and dynamic capillarity 

      Mitra, K; Köppl, T.; Pop, Iuliu Sorin; van Duijn, Duijn; Helmig, Rainer (Journal article; Peer reviewed, 2020)
      In this work, we study the behavior of saturation fronts for two-phase flow through a long homogeneous porous column . In particular, the model includes hysteresis and dynamic effects in the capillary pressure and hysteresis ...
    • Global existence of weak solutions to unsaturated poroelasticity 

      Both, Jakub Wiktor; Pop, Iuliu Sorin; Yotov, Ivan (Journal article; Peer reviewed, 2021)
      We study unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in variably saturated porous media, here modeled by a non-linear extension of Biot’s well-known quasi-static consolidation model. The coupled ...
    • 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 schemes for surfactant transport in porous media 

      Illiano, Davide; Pop, Iuliu Sorin; Radu, Florin Adrian (Journal article; Peer reviewed, 2021)
      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 ...
    • Phase field modeling of precipitation and dissolution processes in porous media: Upscaling and numerical experiments 

      Bringedal, Carina; Wolff, Lars V.O.N.; Pop, Iuliu Sorin (Journal article; Peer reviewed, 2020)
      We consider a model for precipitation and dissolution in a porous medium, where ions transported by a fluid through the pores can precipitate at the pore walls and form mineral. Also, the mineral can dissolve and become ...
    • 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 ...