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Jan Martin  Nordbotten's picture

Jan Martin Nordbotten

Professor
  • E-mailJan.Nordbotten@uib.no
  • Phone+47 909 65 990
  • Visitor Address
    Realfagbygget, Allégt. 41
  • Postal Address
    Postboks 7803
    5020 Bergen

Jan Martin Nordbotten was the youngest ever to complete a PhD in Norway, and the third-youngest professor. He currently leads the porous media research group in the Department of Mathematics at the University of Bergen, and holds a visiting appointment at the Department of Civil and Environmental Engineering at Princeton University. Nordbotten is a recipient of both national and international awards for his research, and is a former VISTA professor of the Norwegian Academy of Sciences and Letters. Nordbotten’s publications span the whole spectrum of applied mathematics, including both theoretical and numerical methods. His research is applied to topics as diverse as ecohydrology, evolution, medical imaging, porous media and renewable energy.

Please feel free to check out my popular science contributions:

Feel free to explore recent completed PhD and MSc projects in our group.

The following list of publications is autmatically generated based on that national research database CRIStin. 

Academic article
  • 2020. An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters. Computer Methods in Applied Mechanics and Engineering. 22 pages.
  • 2019. Well-posedness of the fully coupled quasi-static thermo-poroelastic equations with nonlinear convective transport. Journal of Mathematical Analysis and Applications. 239-266.
  • 2019. On the optimization of the fixed‐stress splitting for Biot's equations. International Journal for Numerical Methods in Engineering. 179-194.
  • 2019. Mathematics and Medicine: How mathematics, modelling and simulations can lead to better diagnosis and treatments . Lecture Notes in Computational Science and Engineering. 66-82.
  • 2019. Iterative solvers for Biot model under small and large deformation . Computational Geosciences.
  • 2019. Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations. Lecture Notes in Computational Science and Engineering. 49-63.
  • 2019. Finite volume discretization for poroelastic media with fractures modeled by contact mechanics. International Journal for Numerical Methods in Engineering. 644-663.
  • 2019. Consistent MPFA Discretization for Flow in the Presence of Gravity. Water Resources Research. 1-14.
  • 2019. Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems. Journal of Computational and Applied Mathematics.
  • 2019. A singularity removal method for coupled 1D–3D flow models. Computational Geosciences.
  • 2019. A new framework for assessing subject-specific whole brain circulation and perfusion using MRI-based measurements and a multi-scale continuous flow model. PLoS Computational Biology. 1-31.
  • 2018. Upscaling of the coupling of hydromechanical and thermal processes in a quasi-static poroelastic medium. Transport in Porous Media. 137-158.
  • 2018. Unified approach to discretization of flow in fractured porous media. Computational Geosciences. 1-13.
  • 2018. Robust iterative schemes for non-linear poromechanics. Computational Geosciences. 1021-1038.
  • 2018. Robust discretization of flow in fractured porous media. SIAM Journal on Numerical Analysis. 2203-2233.
  • 2018. In vivo detection of chronic kidney disease using tissue deformation fields from dynamic MR imaging. IEEE Transactions on Biomedical Engineering. 1779-1790.
  • 2018. Ecological and evolutionary dynamics of interconnectedness and modularity. Proceedings of the National Academy of Sciences of the United States of America. 750-755.
  • 2018. Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers and Mathematics with Applications. 1479-1502.
  • 2018. Adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of Biot's consolidation model. Computer Methods in Applied Mechanics and Engineering. 264-294.
  • 2018. A heterogeneous multiscale MPFA method for single-phase flows in porous media with inertial effects. Computational Geosciences. 107-126.
  • 2018. A finite-volume discretization for deformation of fractured media. Computational Geosciences. 993-1007.
  • 2017. Robust fixed stress splitting for Biot's equations in heterogeneous media. Applied Mathematics Letters. 101-108.
  • 2017. On the Properties of the Parameter Space of the Generalized Continuum Transport Model for Description of Fluid Flow in Porous Networks. Transport in Porous Media. 673-688.
  • 2017. Modeling and Simulation of Microbial Enhanced Oil Recovery Including Interfacial Area. Transport in Porous Media. 395-413.
  • 2017. High-accuracy phase-field models for brittle fracture based on a new family of degradation functions. Journal of the mechanics and physics of solids. 458-489.
  • 2017. Heterogeneity preserving upscaling for heat transport in fractured geothermal reservoirs. Computational Geosciences. 451-467.
  • 2017. Fractal structures in freezing brine. Journal of Fluid Mechanics. 975-995.
  • 2017. Finite volume methods for elasticity with weak symmetry. International Journal for Numerical Methods in Engineering. 939-962.
  • 2017. Comparison between cell-centered and nodal-based discretization schemes for linear elasticity. Computational Geosciences. 28 pages.
  • 2017. Analytical solutions for aquifer thermal energy storage. Water Resources Research. 1354-1368.
  • 2017. A robust, mass conservative scheme for two-phase flow in porous media including Hoelder continuous nonlinearities. IMA Journal of Numerical Analysis. 884-920.
  • 2017. A 3-D numerical model of the influence of meanders on groundwater discharge to a gaining stream in an unconfined sandy aquifer. Journal of Hydrology. 168-181.
  • 2016. Vertically integrated models for coupled two-phase flow and geomechanics in porous media. Water Resources Research. 1398-1417.
  • 2016. Stable cell-centered finite volume discretization for biot equations. SIAM Journal on Numerical Analysis. 942-968.
  • 2016. Rayleigh–Taylor instability of immiscible fluids in porous media. Continuum Mechanics and Thermodynamics. 721-731.
  • 2016. Physical models for simulation and reconstruction of human tissue deformation fields in dynamic MRI. IEEE Transactions on Biomedical Engineering. 2200-2210.
  • 2016. Efficient water table evolution discretization using domain transformation. Computational Geosciences.
  • 2016. Asymmetric ecological conditions favor Red-Queen type of continued evolution over stasis. Proceedings of the National Academy of Sciences of the United States of America. 1847-1852.
  • 2016. A multiscale multilayer vertically integrated model with vertical dynamics for CO2 sequestration in layered geological formations. Water Resources Research. 6490-6505.
  • 2015. Two-scale preconditioning for two-phase nonlinear flows in porous media. Transport in Porous Media. 485-503.
  • 2015. Plant biomass and soil moisture dynamics: Analytical results. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences.
  • 2015. Non-standard shocks in the Buckley-Leverett equation. Journal of Mathematical Analysis and Applications. 882-895.
  • 2015. Inexact linear solvers for control volume discretizations in porous media. Computational Geosciences. 159-176.
  • 2015. Convergence of a Cell-Centered Finite Volume Discretization for Linear Elasticity. SIAM Journal on Numerical Analysis. 2605-2625.
  • 2015. A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media. Journal of Computational and Applied Mathematics. 134-141.
  • 2014. Physics-based preconditioners for flow in fractured porous media. Water Resources Research. 1357-1373.
  • 2014. Finite volume hydromechanical simulation in porous media. Water Resources Research. 4379-4394.
  • 2014. Dynamics of the interface between immiscible liquids of different densities with low Froude number. Nonlinear Analysis: Real world applications. 361-366.
  • 2014. Convective mixing influenced by the capillary transition zone. Computational Geosciences. 417-431.
  • 2014. Conservative inexact solvers for porous media flow. Lecture Notes in Computational Science and Engineering. 333-340.
  • 2014. Cell-centered finite volume discretizations for deformable porous media. International Journal for Numerical Methods in Engineering. 399-418.
  • 2014. Capturing the coupled hydro-mechanical processes occurring during CO2 injection – example from In Salah. Energy Procedia. 3416-3424.
  • 2014. Analytical solutions for two-phase subsurface flow to a leaky fault considering vertical flow effects and fault properties. Water Resources Research. 3536-3552.
  • 2014. Analysis of control volume heterogeneous multiscale methods for single phase flow in porous media. Multiscale Modeling & simulation. 335-363.
  • 2013. Instant convolution shadows for volumetric detail mapping. ACM Transactions on Graphics. 154:1-154:18.
  • 2013. Influence of natural convection in a porous medium when producing from borehole heat exchangers. Water Resources Research. 4927-4938.
  • 2013. Influence of capillary pressure and trapping hysteresis on large-scale CO2 migration. Journal of Coupled Systems and Multiscale Dynamics. 442-458.
  • 2013. Impact of capillary hysteresis and trapping on vertically integrated models for CO2 storage. Advances in Water Resources. 465-474.
  • 2013. Efficient simulation of geothermal processes in heterogeneous porous media based on exponential Rosenbrock-Euler method and Rosenbrock-type methods. Advances in Water Resources. 250-262.
  • 2013. Domain decomposition strategies for nonlinear flow problems in porous media. Journal of Computational Physics. 439-451.
  • 2013. Auxiliary variables for 3D multiscale simulations in heterogeneous porous media. Journal of Computational Physics. 141-153.
  • 2012. Uncertainties in practical simulation of CO2 storage. International Journal of Greenhouse Gas Control. 234-242.
  • 2012. Tensor relative permeabilities: Origin, modeling and numerical discretization. International Journal of Numerical Analysis & Modeling. 701-724.
  • 2012. Initial evaluation of advantageous synergies associated with simultaneous brine production and CO2 geological sequestration. International Journal of Greenhouse Gas Control. 90-100.
  • 2012. Impact of top-surface morphology on CO2 storage capacity. International Journal of Greenhouse Gas Control. 221-235.
  • 2012. Estimating effective rates of convective mixing from commercial-scale injection. Environmental Earth Sciences. 527-535.
  • 2012. Effects of a capillary transition zone on the stability of a diffusive boundary layer. IMA Journal of Applied Mathematics. 771-787.
  • 2012. Effect of mean network coordination number on dispersivity characteristics. Transport in Porous Media. 447-463.
  • 2012. Application of simplified models to CO2 migration and immobilization in large-scale geological systems. International Journal of Greenhouse Gas Control. 72-84.
  • 2012. Applicability of vertical-equilibrium and sharp-interface assumptions in CO2 sequestration modeling. International Journal of Greenhouse Gas Control. 134-147.
  • 2012. An efficient multi-point flux approximation method for Discrete Fracture–Matrix simulations. Journal of Computational Physics. 3784-3800.
  • 2012. An ecohydrological approach to predicting hillslope-scale vegetation patterns in dryland ecosystems. Water Resources Research. 18 pages.
  • 2012. A methodology to estimate maximum probable leakage along old wells in a geological sequestration operation. International Journal of Greenhouse Gas Control. 39-47.
  • 2011. Vertically averaged approaches for CO2 migration with solubility trapping. Water Resources Research. 14 pages.
  • 2011. SUCCESS: SUbsurface CO2 storage–Critical elements and superior strategy. Energy Procedia. 6117-6124.
  • 2011. Quantifying Transient Soil Moisture Dynamics Using Multipoint Direct-Current Resistivity in Homogeneous Sand. Vadose Zone Journal. 286-298.
  • 2011. Numerical Simulation Studies of the Long-term Evolution of a CO2 Plume in a Saline Aquifer with a Sloping Caprock. Transport in Porous Media. 135-151.
  • 2011. Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids. Computational Geosciences. 587-602.
  • 2011. Linear and nonlinear convection in porous media between coaxial cylinders. Physics of Fluids. 11 pages.
  • 2011. Impact of the capillary fringe in vertically integrated models for CO2 storage. Water Resources Research.
  • 2011. Field-scale application of a semi-analytical model for estimation cif CO2 and brine leakage along old wells. International Journal of Greenhouse Gas Control. 257-269.
  • 2011. Field-case simulation of CO2-plume migration using vertical-equilibrium models. Energy Procedia. 3801-3808.
  • 2010. Hydrologic variability and its influence on long-term peat dynamics. Water Resources Research.
  • 2010. Appropriate choice of average pressure for upscaling relative permeability in dynamic flow conditions. SPE Journal. 228-237.
  • 2010. An ecohydrological approach to predicting regional woody species distribution patterns in dryland ecosystems. Advances in Water Resources. 215-230.
  • 2010. A posteriori error estimates for approximate solutions of Barenblatt-Biot poroelastic model. Computational Methods in Applied Mathematics. 302-314.
  • 2010. A new finite-volume approach to efficient discretization on challenging grids. SPE Journal. 658-669.
  • 2009. Vertical Equilibrium with Sub-scale Analytical Methods for Geological CO2 Sequestration. Computational Geosciences. 469-481.
  • 2009. Sufficient criteria are necessary for monotone control volume methods. Applied Mathematics Letters. 1178-1180.
  • 2009. Practical Modeling Approaches for Geological Storage of Carbon Dioxide. Ground Water. 627-638.
  • 2009. On reproducing uniform flow exactly on general hexahedral cells using one degree of freedom per surface. Advances in Water Resources. 264-267.
  • 2009. Multiscale methods for multiphase flow in porous media. Lecture Notes in Computational Science and Engineering. 39-50.
  • 2009. Model for CO2 leakage including multiple geological layers and multiple leaky wells. Environmental Science and Technology. 743-749.
  • 2009. Adaptive variational multiscale methods for multiphase flow in porous media. Multiscale Modeling & simulation. 1455-1473.
  • 2009. A benchmark study on problems related to CO2 storage in geologic formations. Summary and discussion of the results. Computational Geosciences. 409-434.
  • 2008. Stability analysis of probabilistic soil moisture dynamics. Advances in Water Resources. 418-423.
  • 2008. On the relationship between the multiscale finite-volume method and domain decomposition preconditioners. Computational Geosciences. 367-376.
  • 2008. On the definition of macroscale pressure for multiphase flow in porous media. Water Resources Research. 8 pages.
  • 2008. Determining effective wellbore permeability from a field pressure test: a numerical analysis of detection limits. Environmental Geology. 1207-1215.
  • 2008. A compact multipoint flux approximation method with improved robustness. Numerical Methods for Partial Differential Equations. 1329-1360.
  • 2007. Stochastic coupling of rainfall and biomass dynamics. Water Resources Research. 7 pages.
  • 2007. Monotonicity of control volume methods. Numerische Mathematik. 255-288.
  • 2007. Inverse scale spaces for nonlinear regularization. Journal of Mathematical Imaging and Vision. 41-50.
  • 2007. Interpretation of macroscale variables in Darcy's law. Water Resources Research. 9 pages.
  • 2006. Similarity solutions for fluid injection into confined aquifers. Journal of Fluid Mechanics. 307-327.
  • 2006. Non-uniqueness of evapotranspiration due to spatial heterogeneity of plant species. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. 2359-2371.
  • 2006. An improved analytical solution for interface upconing around a well. Water Resources Research. 10 pages.
  • 2005. Semi-Analytical Solution for CO2 Leakage through an Abandoned Well. Environmental Science and Technology. 602-611.
  • 2005. Monotonicity Conditions for Control Volume Methods on Uniform Parallelogram Grids in Homogeneous Media. Computational Geosciences. 61-72.
  • 2005. Injection and Storage of CO2 in Deep Saline Aquifers: Analytical Solution for CO2 Plume Evolution During Injection. Transport in Porous Media. 339-360.
  • 2005. Discretization on quadrilateral grids with improved monotonicity properties. Journal of Computational Physics. 744-760.
  • 2004. Analytical solutions for leakage rates through abandoned wells. Water Resources Research. art. no.-W04204.
Lecture
  • 2015. Fracture propagation in Enhanced Geothermal Systems.
  • 2010. An integrated fracture and continuum model for simulating heat and mass transfer in geothermal systems.
Academic lecture
  • 2019. The mathematical structure of coupled 1D-3D flow models .
  • 2019. Reduced complexity modelling of CO2 leakage through faults.
  • 2019. Numerical Modeling of Fracture Reactivation in a Three-dimensional Domain Based on a Coulomb Friction Law.
  • 2019. Monolithic and Splitting Based Solution Schemes for Nonlinear Quasi-static Thermo-poroelasticity.
  • 2019. Mixed-dimensional discrete fracture matrix models with heterogeneous discretization and non-matching grids.
  • 2019. Coupled 1D-3D flow models .
  • 2019. Consistent discretization of flow for inhomogeneous gravitational fields.
  • 2019. Challenges in Modelling the Anisotropic Poroelastoplastic Behaviour of Fractured Rocks as Homogenized Media.
  • 2019. A study of blood flow regulation on collateral circulation using multiscale flow model.
  • 2018. Well Modelling By Means Of Coupled 1D-3D Flow Models .
  • 2018. Viscous fingering in fractured porous media.
  • 2018. Upscaling of coupled geomechanics, flow, and heat in a poroelastic medium in the quasi-static situation.
  • 2018. Unified modeling and discretization of flow in fractured porous media.
  • 2018. The Mathematical Structure of Coupled 1D-3D Models.
  • 2018. Mixed-dimensional models for materials with thin layers.
  • 2018. Mixed-dimensional models for materials with thin layers.
  • 2018. A general framework for heterogeneous discretizations in mixed-dimensional single-phase flow.
  • 2017. Solution strategies for the coupling of mixed dimensional problems.
  • 2017. Solution strategies for a 3D-1D coupling model.
  • 2017. Modeling, structure, and discretization of mixed-dimensional PDE.
  • 2017. Hybrid FE-FV scheme for modeling pressure-induced fracture propagation in porous media using a phase-field approach.
  • 2017. High-accuracy phase-field models for brittle fracture based on a new family of degradation functions.
  • 2017. Finite volume discretizations of poro-elasticity in high­ contrast media.
  • 2016. Stable and Robust Finite Volume Discretization of Biot’s Equations.
  • 2016. A weakly symmetric finite volume method for elasticity with application to fractures in porous media.
  • 2015. Incorporating Geological Uncertainty in Error Control for Linear Solvers.
  • 2013. Quantifying storage capacity using upscaled models for CO2 storage.
  • 2012. Exponential Euler Time Integrator for Simulation of Geothermal Processes in Heterogeneous Porous Media.
  • 2012. A MPFA approach for simulation of fluid flow and heat transfer in fractured reservoirs.
  • 2011. Discrete Fracture Matrix models for modelling heat and mass transfer in geothermal reservoirs.
  • 2011. Challenges in mathematical modeling and numerical simulation of geothermal systems.
  • 2011. An efficient Multi-Point-Flux-Approximation (MPFA) approach to Discrete Fracture Matrix (DFM) flow models.
  • 2010. Convection cells in porous media. Seminar on flow in porous media and multiscale methods.
  • 2010. A numerical modell of an enhanced geothermal system.
  • 2007. Multipoint flux discretization techniques for general media and scale issues.
  • 2007. Convergence and monotonicity properties of MPFA methods.
  • 2007. A new finite volume approach to efficient discretization on challenging grids.
  • 2006. Threshold scales for spatially averaged soil moisture and evapotranspiration with rainfall heterogeneity.
  • 2006. Streamline methods on fault adapted grids for risk assessment of storage of CO2 in geological formations.
  • 2006. Significance of dipping angle on CO2 plume migration in deep saline aquifers.
  • 2006. On the definition of macro-scale pressure for multi-phase flow in porous media.
  • 2006. Monotonicity of control-volume methods.
  • 2006. Control-volume discretization of elliptic operators on general grids.
  • 2006. Analysis of potential CO2 leakage through abandoned wells using a semi-anlytical model.
  • 2006. Analysis of plume extent using analytical solutions for CO2 storage.
  • 2006. A risk assessment tool to quantify CO2 leakage potential through wells in mature sedimentary basins.
  • 2005. Properties of MPFA methods on quadrilateral grids.
  • 2005. Monotonicity Investigation of Various MPFA Methods onChallenging Grids and Medium Heterogeneities.
  • 2005. Modeling Critical Leakage Pathways in a Risk Assessment Framework: Representation of Abandoned Wells.
  • 2005. Control-volume discretizations compatible with physics.
  • 2004. Recent advances for MPFA methods.
  • 2004. Quantitative estimation of CO2 leakage from geological storage: Analytical models, numerical models, and data needs.
  • 2004. Evaluation of the spread of acid gas plumes injected in deep saline aquifers in western Canada as an analogue to CO2 injection in continental sedimentary basins.
  • 2003. Monotonicity Conditions for Control Volume Methods on General Grids; Application to MPFA.
Editorial
  • 2016. Editorial: Special Issue on “NUPUS: Non-linearities and Upscaling in PoroUS Media”. Transport in Porous Media. 237-240.
Academic anthology/Conference proceedings
  • 2019. Numerical Mathematics and Advanced Applications ENUMATH 2017. Springer Berlin/Heidelberg.
Popular scientific article
  • 2010. Klasseromsforsøk om lagring av CO2 under havbunnen. Naturfag. 66-67.
Feature article
  • 2012. Matematikk som samfunnsfag. Bergens Tidende.
  • 2012. Kan CO2 lagres i undergrunnen? Morgenbladet.
  • 2008. Utopiske Greenpeace. Dagbladet.
  • 2007. Geotermisk energi - glemt i energidebatten? Bergens Tidende.
Doctoral dissertation
  • 2019. Upscaling, analysis, and iterative numerical solution schemes for thermo-poroelasticity.
  • 2019. Phase-field Modeling and Simulation of Brittle Fracture.
  • 2018. Numerical modeling of shear stimulation in naturally fractured geothermal reservoirs.
  • 2018. Model development for efficient simulation of CO2 storage.
  • 2018. Conforming Discretizations of Mixed-Dimensional Partial Differential Equations.
  • 2017. Multiscale analysis of selected problems in fluid dynamics.
  • 2015. Solution strategies for nonlinear conservation laws.
  • 2013. Multiscale simulation of flow and heat transport in fractured geothermal reservoirs.
  • 2004. Sequestration of Carbon in Saline Aquifers - Mathematical and Numerical Analysis.
Documentary
  • 2019. CO2-lagringsforsøk.
Academic chapter/article/Conference paper
  • 2019. Anisotropic Poroelastoplastic Constitutive Model of Fractured Rocks.
  • 2017. Iterative Methods for Coupled Flow and Geomechanics in Unsaturated Porous Media.
  • 2017. A Non-standard Model for Microbial Enhanced Oil Recovery Including the Oil-water Interfacial Area .
  • 2013. Multiscale simulation of flow and heat transport in fractured geothermal reservoirs: inexact solvers and improved transport upscaling.
  • 2013. Influence of convection on production from borehole heat exchangers.
  • 2012. Mass conservative domain decomposition for porous media flow. 23 pages.
  • 2012. Mass Conservative Domain Decomposition for Fractured Porous Media.
  • 2012. MULTISCALE SIMULATION OF NON-DARCY FLOWS. 8 pages.
  • 2012. Exponential Euler Time Integrator for Simulation of Geothermal Processes in Heterogeneous Porous Media. 8 pages.
  • 2010. Variational and heterogeneous multiscale methods. 15 pages.
  • 2010. An integrated fracture and continuum model for simulating heat and mass transfer in geothermal systems.
  • 2010. A Multiscale Framework for Simulating Multi-phase Flow on Flexible Grids.
  • 2006. A compact MPFA method with improved robustness. 12 pages.
Abstract
  • 2007. Geological storage as a carbon mitigation option. Geochimica et Cosmochimica Acta.
Academic literature review
  • 2015. Status of CO<sub>2</sub> storage in deep saline aquifers with emphasis on modeling approaches and practical simulations. 6846-6892.

More information in national current research information system (CRIStin)