Home
Kundan Kumar's picture

Kundan Kumar

Associate Professor
  • E-mailkundan.kumar@uib.no
  • Phone+47 55 58 48 64004793049146
  • 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.

 

I have finished two courses in Pedagogy from Karlstad University, Sweden. These two courses are Teaching in Higher Education I and Supervising Doctoral and Licentiate Students. This corresponds to a total of 10 full weeks of training, that is, 400 hours of training (15 ECTS).

University of Bergen, Department of Mathematics

Responsible lecturer for Continuum Mechanics, Spring 2020, Spring 2021, Spring 2022, Spring 2023

Responsible lecturer for Numerical Linear Algebra, Fall 2020, Fall 2021

Responsible lecturer for Computational Science II, Spring 2015, Spring 2016, Spring 2017, Spring 2018

Responsible lecturer for Finite Element Analysis, Fall 2015, Fall 2017, Fall 2022

Responsible lecturer for Vector and Tensor Analysis, Fall 2016

Co-responsible (Main responsible: Prof. Helge Dahle) for Ordinary Differential Equations, Spring 2023

Karlstad University Sweden, Department of Mathematics and Computer Science

Responsible lecturer for Ordinary Differential Equations, Fall 2018,

Responsible lecturer for Advanced Linear Algebra, Spring 2019,

Responsible lecturer for Complex Analysis and Transforms, Spring 2019

Optimization, Spring 2019

Teaching at Eindhoven University of Technology, The Netherlands

Instructor, Advanced Calculus 2008-09, 2009-10, 2010-11.

Instructor, Vector Calculus 2009-2010.

 

Academic article
  • Show author(s) (2024). Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics. Mathematics and mechanics of solids.
  • Show author(s) (2023). Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media. Numerical Methods for Partial Differential Equations.
  • Show author(s) (2022). Field-scale impacts of long-term wettability alteration in geological CO<inf>2</inf> storage. International Journal of Greenhouse Gas Control. 16 pages.
  • Show author(s) (2022). Dimensional reduction of a fractured medium for a two-phase flow. Advances in Water Resources.
  • Show author(s) (2022). Convergence of single rate and multirate undrained split iterative schemes for a fractured biot model. Computational Geosciences. 975-994.
  • 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) (2021). Modeling of relative permeabilities including dynamic wettability transition zones. Journal of Petroleum Science and Engineering. 14 pages.
  • Show author(s) (2021). Dimensional reduction of a fractured medium for a polymer EOR model. Computational Geosciences. 1753-1773.
  • Show author(s) (2021). A Mixed Approach to the Poisson Problem with Line Sources. SIAM Journal on Numerical Analysis. 1117-1139.
  • 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). Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. Journal of Computational Physics.
  • 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) (2022). py-micp: An Open-Source Simulation Workflow for Field-Scale Application of Microbially Induced Calcite Precipitation Technology for Leakage Remediation.
  • Show author(s) (2022). Modeling and Simulation of Wettability Alteration for CO2 Storage.
  • Show author(s) (2022). Modeling and Simulation of Long-term Wettability Alteration on CO2 Storage Efficiency and Containment.
  • Show author(s) (2021). ad-micp: A third-party module for MRST to study CO2 leakage remediation by microbially induced calcite precipitation.
  • Show author(s) (2021). Using MRST for Solving Multiphase Flow Models in Porous Media.
  • Show author(s) (2021). Upscaling of flow models in a fractured media.
  • Show author(s) (2021). Robust block-partitioned solvers for poroelasticity derived from its gradient flow structures.
  • Show author(s) (2021). Robust block-partitioned solvers for flow in deformable porous media via alternating minimization.
  • Show author(s) (2021). Numerical studies of microbially induced calcite precipitation at the field scale.
  • Show author(s) (2021). Numerical studies of long-term wettability alteration effects in CO2 storage applications.
  • Show author(s) (2021). Numerical studies of CO2 leakage remediation by MICP-based plugging technology.
  • Show author(s) (2021). Monotonicity of Effective Tensors with Respect to Geometric Perturbations.
  • Show author(s) (2021). Homogenization of Reactive Flows in Porous Media.
  • Show author(s) (2021). Block-partitioned solvers for poromechanics via gradient flows and minimization.
  • Show author(s) (2020). Robust Block-Partitioned Solvers for Poroviscoelasticity.
  • Show author(s) (2020). Numerical simulations of biofilms in core samples: MEOR and MICP.
  • Show author(s) (2020). Modeling and Simulations of Microbially Induced Calcite Precipitation.
  • Show author(s) (2019). The mathematical structure of coupled 1D-3D flow models .
  • Show author(s) (2019). Mathematical modelling of the bio-plug technology: laboratory experiments, upscaling, and numerical simulations.
  • 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.
  • Show author(s) (2017). An upscaled model for permeable biofilm formation in a thin strip.
Editorial
  • Show author(s) (2021). Guest Editorial to the special issue: Computational mathematics aspects of flow and mechanics of porous media: State-of-the-art computational methods in the mechanics and flow in porous media. Computational Geosciences. 601-602.
  • Show author(s) (2019). Preface. Lecture Notes in Computational Science and Engineering. v-vi.
  • 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.
Software
  • Show author(s) (2021). ad-micp: A module to study CO2 leakage remediation by microbially induced calcite precipitation (MICP).
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.
Documentary
  • Show author(s) (2022). NFR Toppforsk project Thermo-Mechanical Energy Storage.
Academic chapter/article/Conference paper
  • Show author(s) (2023). Thermodynamic analysis of a multi-evaporator refrigeration cycle using a two-phase ejector as an expansion device. 12 pages.
  • Show author(s) (2021). Numerical studies of long-term wettability alteration effects in CO2 storage applications. 5 pages.
  • Show author(s) (2021). Numerical studies of CO2 leakage remediation by MICP-based plugging technology. 7 pages.
  • 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.
  • Show author(s) (2019). Biofilms in porous media: laboratory experiments, mathematical modeling and upscaling.
  • Show author(s) (2018). Mathematical modelling of bacterial growth at different scales: numerical simulations and laboratory experiments.
  • Show author(s) (2018). Mathematical modeling of biofilm formation: from the pore-scale to the core-scale.
  • Show author(s) (2017). A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments.
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

2016-2017

NFR-DAAD (PI, UoB-University of Erlangen, Germany): Upscaling of Evolving Microstructures and its Applications, (80k NOK).

2015-2016

SIU Project  (PI, UoB-Russian Academy of Sciences, St. Petersburg). An extensive collaborative project on education, research and training with 
Russian Academy of Sciences, St Petersburg, Russia, CPRU 2015/10040, (147k NOK).

2017-2020

NFR-Petromaks2  (Co-applicant, UniResearch CIPR-UoB): EOR upscaling - from lab to field, 2 PhD at UoB); main-adviser for the PhD,  (24M NOK).

2017-2020

NFR-CLIMIT  (Co-applicant, UniResearch CIPR-UoB): Efficient models for Microbially Induced CAlcite Precipitation as a seal for CO2 storage (MICAP), (8M NOK).

2016-2020

NFR-Toppforsk  (Co-applicant): Thermo-Mechanical Subsurface Energy Storage (TheMSeS) (4 PhD, 4 PostDocs); main adviser for 1 PhD, (25M NOK).

2016-2019

NFR-Petromaks2  (Co-applicant, Collaboration UniResearch CIPR-UoB): Improving microbial selective plugging technology through experimentally based modelling and simulation (IMMENS) (1 PhD at UoB); co-adviser for the PhD, (10M NOK).

2016-2019

NFR-CLIMIT  (Co-applicant, UniResearch CIPR-UoB): Fundamentals of CO2- Hydrocarbon Interactions for CO2 storage with enhanced oil recovery (CHI).(7M NOK).

2016-2017

NFR-DAAD  (Co-applicant, UoB-Federal Army University of Hamburg, Germany): Efficient discretizations and fast solvers for poroelasticity, (60k NOK).

2016-2019

UoB/Statoil Project  (Co-author): Experimentally based modelling of colloid transport in multiphase porous media (EPOCH) (1 PostDoc). WP leader, (3.5M NOK).

2020-2022

PI: Strategisk program for internasjonalt forskningssamarbeid, SPIRE UoB, (60k NOK)

 

2021-2026

VISTA Center for Coupled Subsurface Dynamics, UoB, Head of one of three scientific pillars, (25 M NOK)

2023- 2025

Project manager and PI, Modelling and Solution Strategies for the Subsurface Deformations, (200k NOK). Akademiaavtalen.

 

2022-2028

Deputy Head of Work Package 1, Center for Sustainable Subsurface Resources, one of three current petroleum research centers (PETROCENTER), Main supervisor of 1 PhD student.