Blar i Bergen Open Research Archive på forfatter "Nordbotten, Jan Martin"
-
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 ... -
An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters
Brun, Mats Kirkesæther; Wick, Thomas; Berre, Inga; Nordbotten, Jan Martin; Radu, Florin Adrian (Journal article; Peer reviewed, 2020)This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model ... -
Klasseromsforsøk om lagring av CO2 under havbunnen
Nordbotten, Jan Martin; Rygg, Kristin (Journal article, 2010) -
Linear and nonlinear convection in porous media between coaxial cylinders
Bringedal, Carina; Berre, Inga; Nordbotten, Jan Martin; Rees, D. Andrew S. (Peer reviewed; Journal article, 2011)We uncover novel features of three-dimensional natural convection in porous media by investigating convection in an annular porous cavity contained between two vertical coaxial cylinders. The investigations are made using ... -
Mass Conservative Domain Decomposition for Porous Media Flow
Nordbotten, Jan Martin; Keilegavlen, Eirik; Sandvin, Andreas (Chapter, 2012-03-28) -
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 minimalist model for coevolving supply and drainage networks
Anand, Shashank Kumar; Hooshyar, Milad; Nordbotten, Jan Martin; Porporato, Amilcare (Journal article; Peer reviewed, 2021)Numerous complex systems, both natural and artificial, are characterized by the presence of intertwined supply and/or drainage networks. Here, we present a minimalist model of such coevolving networks in a spatially ... -
A Mixed Approach to the Poisson Problem with Line Sources
Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (Journal article; Peer reviewed, 2021)In this work we consider the dual-mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is nonstandard, as the line source causes the solutions to be ... -
Mixed-dimensional poromechanical models of fractured porous media
Boon, Wietse; Nordbotten, Jan Martin (Journal article; Peer reviewed, 2022)We combine classical continuum mechanics with the recently developed calculus for mixed-dimensional problems to obtain governing equations for flow in, and deformation of, fractured materials. We present models in both the ... -
Modeling and discretization of flow in porous media with thin, full-tensor permeability inclusions
Starnoni, Michele; Berre, Inga; Keilegavlen, Eirik; Nordbotten, Jan Martin (Journal article; Peer reviewed, 2021)When modeling fluid flow in fractured reservoirs, it is common to represent the fractures as lower-dimensional inclusions embedded in the host medium. Existing discretizations of flow in porous media with thin inclusions ... -
Modeling the Process of Speciation Using a Multiscale Framework Including A Posteriori Error Estimates
Brun, Mats Kirkesæther; Ahmed, Elyes; Nordbotten, Jan Martin; Stenseth, Nils Christian (Journal article; Peer reviewed, 2022)This paper concerns the modeling and numerical simulation of the process of speciation. In particular, given conditions for which one or more speciation events within an ecosystem occur, our aim is to develop the necessary ... -
Monolithic and splitting solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport
Brun, Mats Kirkesæther; Ahmed, Elyes; Berre, Inga; Nordbotten, Jan Martin; Radu, Florin Adrian (Journal article; Peer reviewed, 2020)This paper concerns monolithic and splitting-based iterative procedures for the coupled nonlinear thermo-poroelasticity model problem. The thermo-poroelastic model problem we consider is formulated as a three-field system ... -
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 ... -
Multiscale Simulation of Non-Darcy Flows
Alyaev, Sergey; Keilegarden, Eirik; Nordbotten, Jan Martin (Chapter; Peer reviewed, 2012-06)In this work we present control volume multiscale methods which address problems on the interaction between pore scale and Darcy scale. For the case when linear equations govern the ow on the pore scale our solution converges ... -
A new framework for assessing subject-specific whole brain circulation and perfusion using MRI-based measurements and a multi-scale continuous flow model
Hodneland, Erlend; Hanson, Erik Andreas; Sævareid, Ove; Nævdal, Geir; Lundervold, Arvid; Solteszova, Veronika; Zanna, Antonella; Deistung, Andreas; Reichenbach, Jürgen; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2019-06-25)A large variety of severe medical conditions involve alterations in microvascular circulation. Hence, measurements or simulation of circulation and perfusion has considerable clinical value and can be used for diagnostics, ... -
A New Preconditioner for Iterative Phase Splitting Routines
Nordbotten, Jan Martin (Master thesis, 2002)This thesis proposes a new, faster, non-iterative phase split estimate for multi component mixtures, and compares it with the previously published method of Wang and Stenby, in terms of their suitability as possible ... -
Non-standard shocks in the Buckley-Leverett equation
Kalisch, Henrik; Mitrovic, Darko; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2015-08)It is shown how delta shock waves which consist of Dirac delta distributions and classical shocks can be used to construct non-monotone solutions of the Buckley–Leverett equation. These solutions are interpreted using a ... -
A nonlinear multi-scale model for blood circulation in a realistic vascular system
Qohar, Ulin Nuha Abdul; Munthe-Kaas, Antonella Zanna; Nordbotten, Jan Martin; Hanson, Erik Andreas (Journal article; Peer reviewed, 2021)In the last decade, numerical models have become an increasingly important tool in biological and medical science. Numerical simulations contribute to a deeper understanding of physiology and are a powerful tool for better ... -
Numerical Simulation Studies of the Long-term Evolution of a CO2 Plume in a Saline Aquifer with a Sloping Caprock
Pruess, Karsten; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2011-02-02)We have used the TOUGH2-MP/ECO2N code to perform numerical simulation studies of the long-term behavior of CO2 stored in an aquifer with a sloping caprock. This problem is of great practical interest, and is very challenging ... -
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. ...