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Kundan Kumar's picture

Kundan Kumar

Associate Professor
Department of Mathematics
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  • 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
  • List, Florian; Kumar, Kundan; Pop, Iuliu Sorin; Radu, Florin Adrian. 2020. Rigorous Upscaling of Unsaturated Flow in Fractured Porous Media. SIAM Journal on Mathematical Analysis. 239-276.
  • Kumar, Kundan; List, Florian; Pop, Iuliu Sorin; Radu, Florin Adrian. 2020. Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. Journal of Computational Physics. 21 pages.
  • Marban, David Landa; Bødtker, Gunhild; Kumar, Kundan; Pop, Iuliu Sorin; Radu, Adrian Florin. 2020. An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube. Transport in Porous Media. 83-112.
  • Landa Marban, David; Bødtker, Gunhild; Kumar, Kundan; Pop, Iuliu Sorin; Radu, Florin Adrian. 2020. An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube. Transport in Porous Media. 30 pages.
  • Ye, Ruichao; Kumar, Kundan; de Hoop, Maarten V.; Campillo, Michel. 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.
  • Almani, T; Kumar, Kundan; Singh, G.; Wheeler, MF. 2019. Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium. Computers and Mathematics with Applications. 1-18.
  • Storvik, Erlend; Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin; Radu, Florin Adrian. 2019. On the optimization of the fixed‐stress splitting for Biot's equations. International Journal for Numerical Methods in Engineering. 179-194.
  • Landa-Marbán, David; Pop, Iuliu Sorin; Kumar, Kundan; Radu, Florin Adrian. 2019. Numerical Simulation of Biofilm Formation in a Microchannel. Lecture Notes in Computational Science and Engineering. 799-807.
  • Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin; Pop, Iuliu Sorin; Radu, Florin Adrian. 2019. Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations. Lecture Notes in Computational Science and Engineering. 49-63.
  • Almani, Tameem; Manea, AM; Kumar, Kundan; Dogru, Ali H. 2019. Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences. 1-19.
  • Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin. 2019. A singularity removal method for coupled 1D–3D flow models. Computational Geosciences.
  • Endo Kokubun, Max Akira; Radu, Florin Adrian; Keilegavlen, Eirik; Kumar, Kundan; Spildo, Kristine. 2018. Transport of polymer particles in oil–water flow in porous media: Enhancing oil recovery. Transport in Porous Media. 1-19.
  • Borregales Reveron, Manuel Antonio; Radu, Florin Adrian; Kumar, Kundan; Nordbotten, Jan Martin. 2018. Robust iterative schemes for non-linear poromechanics. Computational Geosciences. 1021-1038.
  • Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin; Radu, Florin Adrian. 2018. Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers and Mathematics with Applications. 1479-1502.
  • Landa-Marban, David; Liu, Na; Pop, Iuliu Sorin; Kumar, Kundan; Pettersson, Per; Bødtker, Gunhild; Skauge, Tormod; Radu, Florin Adrian. 2018. A pore-scale model for permeable biofilm: Numerical simulations and laboratory experiments. Transport in Porous Media. 643-660.
  • Borregales Reveron, Manuel Antonio; Kumar, Kundan; Radu, Florin Adrian; Rodrigo, Carmen; Gaspar, Francisco José. 2018. A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model. Computers and Mathematics with Applications. 1466-1478.
  • Both, Jakub; Borregales Reveron, Manuel Antonio; Kumar, Kundan; Nordbotten, Jan Martin; Radu, Florin Adrian. 2017. Robust fixed stress splitting for Biot's equations in heterogeneous media. Applied Mathematics Letters. 101-108.
  • Vasilyev, Leonid; Nordbotten, Jan Martin; Radu, Florin Adrian; Kumar, Kundan. 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.
  • Bringedal, Carina; Kumar, Kundan. 2017. Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow. Transport in Porous Media. 553-577.
  • Almani, Tameem; Kumar, Kundan; Wheeler, M.F. 2017. Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Computational Geosciences. 1157-1172.
  • Pop, Iuliu Sorin; Bogers, Jeroen; Kumar, Kundan. 2017. Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition. Vietnam Journal of Mathematics. 77-102.
  • Radu, Florin Adrian; Kumar, Kundan; Nordbotten, Jan Martin; Pop, Iuliu Sorin. 2017. A robust, mass conservative scheme for two-phase flow in porous media including Hoelder continuous nonlinearities. IMA Journal of Numerical Analysis. 884-920.
  • Kumar, Kundan; Almani, Tameem; Singh, Gurpreet; Wheeler, Mary F. 2016. Multirate undrained splitting for coupled flow and geomechanics in porous media. Lecture Notes in Computational Science and Engineering. 431-440.
  • Kumar, Kundan; Neuss-Radu, Maria; Pop, Iuliu Sorin. 2016. Homogenization of a pore scale model for precipitation and dissolution in porous media. IMA Journal of Applied Mathematics. 877-897.
  • Girault, Vivette; Kumar, Kundan; Wheeler, Mary Fanett. 2016. Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. Computational Geosciences. 997-1011.
  • Almani, Tameem; Kumar, Kundan; Dogru, Ali H.; Singh, Gurpreet P.; Wheeler, Mary Fanett. 2016. Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Computer Methods in Applied Mechanics and Engineering. 180-207.
  • Radu, Adrian Florin; Nordbotten, Jan Martin; Pop, Iuliu Sorin; Kumar, Kundan. 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.
  • Sepasian, Neda; Kumar, Kundan; Breeuwer, Marcel. 2015. A geometrical approach to find corresponding patches in 3D medical surfaces. Lecture Notes in Computer Science (LNCS). 217-219.
Report
  • Radu, Florin Adrian; Kumar, Kundan; Nordbotten, Jan Martin; Pop, Sorin Iuliu. 2017. A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media. .
Academic lecture
  • Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin. 2019. The mathematical structure of coupled 1D-3D flow models .
  • Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin. 2019. Coupled 1D-3D flow models .
  • Kassa, Abay; Gasda, Sarah; Kumar, Kundan; Radu, Florin Adrian. 2019. Constitutive relations modelling for dynamically altered porous medium.
  • Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin. 2018. Well Modelling By Means Of Coupled 1D-3D Flow Models .
  • Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin. 2018. The Mathematical Structure of Coupled 1D-3D Models.
  • Kassa, Abay; Gasda, Sarah; Kumar, Kundan; Radu, Florin Adrian. 2018. Impact of Wettability Evolution on Dynamic Capillary Pressure.
  • Kassa, Abay; Gasda, Sarah Eileen; Radu, Florin Adrian; Kumar, Kundan. 2018. Impact of Time-Dependent Wettability Alteration on Capillary Pressure.
  • Gasda, Sarah Eileen; Kassa, Abay; Radu, Florin Adrian; Kumar, Kundan. 2018. A Model for Dynamic Capillary Pressure with Time-Dependent Wettability Alteration.
  • Kumar, Kundan; Gjerde, Ingeborg Gåseby; Nordbotten, Jan Martin; Wohlmuth, Barbara. 2017. Solution strategies for the coupling of mixed dimensional problems.
  • Kumar, Kundan; Gjerde, Ingeborg Gåseby; Nordbotten, Jan Martin; Wohlmuth, Barbara. 2017. Solution strategies for a 3D-1D coupling model.
  • Gjerde, Ingeborg Gåseby; Kumar, Kundan. 2017. Mixed methods for hierarchical flow models for wells in porous media .
  • Gjerde, Ingeborg Gåseby; Kumar, Kundan. 2017. Mixed methods for hierarchical flow models for wells in porous media .
  • Kumar, Kundan. 2017. Coupled Problems in Porous Media.
Editorial
  • Salama, Amgad; Sun, Shuyu; El Amin, Mohamed F.; Wang, Yi; Kumar, Kundan. 2017. Flow and transport in porous media: a multiscale focus. Geofluids. 1-3.
Academic anthology/Conference proceedings
  • Radu, Florin Adrian; Kumar, Kundan; Berre, Inga; Nordbotten, Jan Martin; Pop, Iuliu Sorin. 2019. Numerical Mathematics and Advanced Applications ENUMATH 2017. Springer Berlin/Heidelberg.
Masters thesis
  • Samaneh, Mofrad Abolpour. 2016. Microbially enhanced techniques for oil recovery and clogging.
  • Abay, Kassa. 2016. Mathematical Modeling of Optimal Control Strategy for Microbial Enhanced Oil Recovery Processes.
Doctoral dissertation
  • Landa-Marbán, David. 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
  • Kassa, Abay; Gasda, Sarah; Kumar, Kundan; Radu, Florin Adrian. 2018. Impact of Wettability Evolution on Dynamic Capillary Pressure.
  • Kumar, Kundan; Ratnayake, R.M. Chandima. 2017. Maintenance Regime Minimum (MRM): State of the Art — Maintaining Offshore Platforms Before Decommissioning. 10 pages.
  • Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin; Radu, Florin Adrian. 2017. Iterative Methods for Coupled Flow and Geomechanics in Unsaturated Porous Media.
Abstract
  • Kassa, Abay; Gasda, Sarah; Kumar, Kundan; Radu, Florin Adrian. 2018. Impact of time-dependent wettability alteration on dynamic capillary pressure. EAGE Fifth CO2 Geological Storage Workshop.
Poster
  • Kassa, Abay; Gasda, Sarah; Kumar, Kundan; Radu, Florin Adrian. 2019. Constitutive relations for dynamic wettability transition zones.
Academic literature review
  • Salama, Amgad; El Amin, Mohamed F.; Kumar, Kundan; Sun, Shuyu. 2017. Flow and transport in tight and shale formations: A review. 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).