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Kundan Kumar

Associate Professor
  • E-mailKundan.Kumar@uib.no
  • Phone+47 55 58 48 64+47 930 49 146
  • Visitor Address
    Allegaten 41
    5007 Bergen
    Room 
    Rfg 4A16
  • Postal Address
    Postboks 7803
    5020 Bergen

My research interests are in developing upscaled models, dimensional reduction and numerical algorithms for  coupled multiphysics processes such as flow and transport in deformable porous media. The reactive flow models lead to changes in the geometry at the pore scale and require non-standard models for describing the processes. I have performed upscaling and dimensional reduction of such reactive processes and developed numerical methods for  solving the upscaled models. I have also worked on scalable algorithms such as domain decomposition techniques for simulating multiphase flow and transport in porous media. In addition, I have worked on the analysis of  iterative and multirate algorithms for solving the  coupled flow and geomechanics problems in a  porous medium.

 

Vector and Tensor Analysis MAT 235, Fall 2016

Finite Element Analysis, Fall 2015

Computational Science II, Spring 2015, Spring 2016 

Academic article
  • Show author(s) 2021. Practical approaches to study microbially induced calcite precipitation at the field scale. International Journal of Greenhouse Gas Control.
  • Show author(s) 2020. Rigorous upscaling of unsaturated flow in fractured porous media. SIAM Journal on Mathematical Analysis. 239-276.
  • Show author(s) 2020. Mathematical modeling, laboratory experiments, and sensitivity analysis of bioplug technology at Darcy scale. SPE Journal. 3120-3137.
  • Show author(s) 2020. Iterative solvers for Biot model under small and large deformations. Computational Geosciences.
  • Show author(s) 2020. Implicit linearization scheme for nonstandard two-phase flow in porous media. International Journal for Numerical Methods in Fluids. 1-17.
  • Show author(s) 2020. Impact of time-dependent wettability alteration on the dynamics of capillary pressure. Advances in Water Resources.
  • Show author(s) 2020. Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem. Computers and Mathematics with Applications.
  • Show author(s) 2020. Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. Journal of Computational Physics. 21 pages.
  • Show author(s) 2020. Analysis of dynamic ruptures generating seismic waves in a self-gravitating planet: An iterative coupling scheme and well-posedness. Quarterly of Applied Mathematics. 485-511.
  • Show author(s) 2020. An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube. Transport in Porous Media. 83-112.
  • Show author(s) 2020. A multi-rate iterative coupling scheme for simulating dynamic ruptures and seismic waves generation in the prestressed earth. Journal of Computational Physics. 1-39.
  • Show author(s) 2019. Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium. Computers and Mathematics with Applications. 1-18.
  • Show author(s) 2019. Splitting method for elliptic equations with line sources. Mathematical Modelling and Numerical Analysis. 1715-1739.
  • Show author(s) 2019. On the optimization of the fixed‐stress splitting for Biot's equations. International Journal for Numerical Methods in Engineering. 179-194.
  • Show author(s) 2019. Numerical Simulation of Biofilm Formation in a Microchannel. Lecture Notes in Computational Science and Engineering. 799-807.
  • Show author(s) 2019. Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations. Lecture Notes in Computational Science and Engineering. 49-63.
  • Show author(s) 2019. Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences. 1-19.
  • Show author(s) 2019. A singularity removal method for coupled 1D–3D flow models. Computational Geosciences.
  • Show author(s) 2018. Transport of polymer particles in oil–water flow in porous media: Enhancing oil recovery. Transport in Porous Media. 1-19.
  • Show author(s) 2018. Robust iterative schemes for non-linear poromechanics. Computational Geosciences. 1021-1038.
  • Show author(s) 2018. Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers and Mathematics with Applications. 1479-1502.
  • Show author(s) 2018. A pore-scale model for permeable biofilm: Numerical simulations and laboratory experiments. Transport in Porous Media. 643-660.
  • Show author(s) 2018. A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model. Computers and Mathematics with Applications. 1466-1478.
  • Show author(s) 2017. Robust fixed stress splitting for Biot's equations in heterogeneous media. Applied Mathematics Letters. 101-108.
  • Show author(s) 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.
  • Show author(s) 2017. Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow. Transport in Porous Media. 553-577.
  • Show author(s) 2017. Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Computational Geosciences. 1157-1172.
  • Show author(s) 2017. Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition. Vietnam Journal of Mathematics. 77-102.
  • Show author(s) 2017. A robust, mass conservative scheme for two-phase flow in porous media including Hoelder continuous nonlinearities. IMA Journal of Numerical Analysis. 884-920.
  • Show author(s) 2016. Multirate undrained splitting for coupled flow and geomechanics in porous media. Lecture Notes in Computational Science and Engineering. 431-440.
  • Show author(s) 2016. Homogenization of a pore scale model for precipitation and dissolution in porous media. IMA Journal of Applied Mathematics. 877-897.
  • Show author(s) 2016. Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. Computational Geosciences. 997-1011.
  • Show author(s) 2016. Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Computer Methods in Applied Mechanics and Engineering. 180-207.
  • Show author(s) 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.
  • Show author(s) 2015. A geometrical approach to find corresponding patches in 3D medical surfaces. Lecture Notes in Computer Science (LNCS). 217-219.
Report
  • Show author(s) 2017. A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media. .
Academic lecture
  • Show author(s) 2020. Robust Block-Partitioned Solvers for Poroviscoelasticity.
  • Show author(s) 2019. The mathematical structure of coupled 1D-3D flow models .
  • Show author(s) 2019. Coupled 1D-3D flow models .
  • Show author(s) 2019. Constitutive relations modelling for dynamically altered porous medium.
  • Show author(s) 2019. Analysis and approximation of coupled 1D-3D flow models.
  • Show author(s) 2018. Well Modelling By Means Of Coupled 1D-3D Flow Models .
  • Show author(s) 2018. The Mathematical Structure of Coupled 1D-3D Models.
  • Show author(s) 2018. Impact of Wettability Evolution on Dynamic Capillary Pressure.
  • Show author(s) 2018. Impact of Time-Dependent Wettability Alteration on Capillary Pressure.
  • Show author(s) 2018. A Model for Dynamic Capillary Pressure with Time-Dependent Wettability Alteration.
  • Show author(s) 2017. Solution strategies for the coupling of mixed dimensional problems.
  • Show author(s) 2017. Solution strategies for a 3D-1D coupling model.
  • Show author(s) 2017. Mixed methods for hierarchical flow models for wells in porous media .
  • Show author(s) 2017. Mixed methods for hierarchical flow models for wells in porous media .
  • Show author(s) 2017. Coupled Problems in Porous Media.
Editorial
  • Show author(s) 2017. Flow and transport in porous media: a multiscale focus. Geofluids. 1-3.
Academic anthology/Conference proceedings
  • Show author(s) 2019. Numerical Mathematics and Advanced Applications ENUMATH 2017. Springer Berlin/Heidelberg.
Masters thesis
  • Show author(s) 2016. Microbially enhanced techniques for oil recovery and clogging.
  • Show author(s) 2016. Mathematical Modeling of Optimal Control Strategy for Microbial Enhanced Oil Recovery Processes.
Doctoral dissertation
  • Show author(s) 2019. Mathematical modeling of microbial enhanced oil recovery with focus on bio-plug technology: from the pore to the core scale.
Academic chapter/article/Conference paper
  • Show author(s) 2018. Impact of Wettability Evolution on Dynamic Capillary Pressure.
  • Show author(s) 2017. Maintenance Regime Minimum (MRM): State of the Art — Maintaining Offshore Platforms Before Decommissioning. 10 pages.
  • Show author(s) 2017. Iterative Methods for Coupled Flow and Geomechanics in Unsaturated Porous Media.
Abstract
  • Show author(s) 2018. Impact of time-dependent wettability alteration on dynamic capillary pressure. EAGE Fifth CO2 Geological Storage Workshop.
Poster
  • Show author(s) 2019. Constitutive relations for dynamic wettability transition zones.
Academic literature review
  • Show author(s) 2017. Flow and transport in tight and shale formations: A review. Geofluids. 1-21.

More information in national current research information system (CRIStin)

Please see attached CV.

At Google scholar https://scholar.google.com/citations?user=rHFW3EAAAAAJ&hl=en


1. Project Manager and PI, Upscaling of Evolving Microstructures and its Applications, NRC-Daad collaboration with University of Erlangen, Germany  (80k NOK).
2. Project Manager and PI, An extensive collaborative project on education, research and training with Russian Academy of Sciences, St Petersburg, Russia, SIU project, CPRU 2015/10040  (147k NOK).
3. Co-applicant,  Thermo-Mechanical Subsurface Energy Storage, Toppforsk (25M NOK).
4. Co-applicant,  Improving microbial selective plugging technology through experimentally based modelling and simulation, Petromaks 2  (9M NOK).
5. Co-applicant,  Fundamentals of CO2-Hydrocarbon Interactions for CO2 storage with enhanced recovery (EOR/EGR) in offshore reservoirs: modeling, numerical methods and upscaling (Project CHI), Klimaforsk (8M NOK).
6. Co-applicant,  Efficient discretizations and fast solvers for poroelasticity, NRC-DAAD collaboration with Helmut-Schmidt-Universit\"at, Germany  (60k NOK).
7. Co-author, Experimentally based modelling of colloid transport in multiphase porous media (EPOCH), Statoil - Akademia Grant (3400k NOK).

8. Co-applicant, EOR upscaling - from lab to field, Petromaks 2 (24M NOK).

9.  Co-applicant,  Efficient models for Microbially Induced CAlcite Precipitation as a seal for CO2 storage (MICAP),  (8M NOK).