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.

 

Poster

• Gürsel, Hasan; Ersland, Geir; Gasda, Sarah Eileen et al. (2024). Modeling the Temporal Dynamics of Formation Damage during Produced Water Re-injection. (external link)
• Landa-Marbán, David; Liu, Na; Pop, Iuliu Sorin et al. (2019). Biofilms in porous media: laboratory experiments, mathematical modeling and upscaling. (external link)
• Kassa, Abay; Gasda, Sarah; Kumar, Kundan et al. (2019). Constitutive relations for dynamic wettability transition zones. (external link)
• Landa-Marbán, David; Liu, Na; Pop, Sorin Iuliu et al. (2018). Mathematical modelling of bacterial growth at different scales: numerical simulations and laboratory experiments. (external link)
• Landa-Marbán, David; Liu, Na; Pop, Iuliu Sorin et al. (2018). Mathematical modeling of biofilm formation: from the pore-scale to the core-scale. (external link)
• Landa-Marbán, David; Liu, Na; Pop, Iuliu Sorin et al. (2017). A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments. (external link)

Academic article

• Kraus, Johannes; Kumar, Kundan; Lymbery, Maria et al. (2024). A fixed-stress splitting method for nonlinear poroelasticity. (external link)
• Kumar, Shridhar; Das, Pratibhamoy; Kumar, Kundan (2024). Adaptive mesh based efficient approximations for Darcy scale precipitation–dissolution models in porous media. (external link)
• Taki, Nadia Skoglund; Kumar, Kundan (2024). Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics. (external link)
• Almani, T.; Kumar, Kundan (2024). Convergence of multirate fixed stress split iterative schemes for a fractured Biot model. (external link)
• Almani, Tameem; Kumar, Kundan; Wheeler, Mary F. (2023). Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media. (external link)
• Kassa, Abay; Gasda, Sarah Eileen; Landa-Marbán, David et al. (2022). Field-scale impacts of long-term wettability alteration in geological CO<inf>2</inf> storage. (external link)
• Almani, T.; Kumar, Kundan (2022). Convergence of single rate and multirate undrained split iterative schemes for a fractured biot model. (external link)
• Dugstad, Martin Sandanger; Kumar, Kundan (2022). Dimensional reduction of a fractured medium for a two-phase flow. (external link)
• Kassa, Abay; Gasda, Sarah E.; Kumar, Kundan et al. (2021). Modeling of relative permeabilities including dynamic wettability transition zones. (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (2021). A Mixed Approach to the Poisson Problem with Line Sources. (external link)
• Dugstad, Martin Sandanger; Kumar, Kundan; Pettersen, Øystein (2021). Dimensional reduction of a fractured medium for a polymer EOR model. (external link)
• Landa-Marbán, David; Tveit, Svenn; Kumar, Kundan et al. (2021). Practical approaches to study microbially induced calcite precipitation at the field scale. (external link)
• List, Florian; Kumar, Kundan; Pop, Iuliu Sorin et al. (2020). Rigorous upscaling of unsaturated flow in fractured porous media. (external link)
• Borregales Reveron, Manuel Antonio; Kumar, Kundan; Nordbotten, Jan Martin et al. (2020). Iterative solvers for Biot model under small and large deformations. (external link)
• Radu, Adrian Florin; Pop, Iuliu Sorin; List, Florian et al. (2020). Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. (external link)
• Kumar, Kundan; Kyas, Svetlana; Nordbotten, Jan Martin et al. (2020). Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem. (external link)
• de Hoop, Maarten V.; Kumar, Kundan; Ye, Ruichao (2020). Analysis of dynamic ruptures generating seismic waves in a self-gravitating planet: An iterative coupling scheme and well-posedness. (external link)
• Kassa, Abay; Kumar, Kundan; Gasda, Sarah et al. (2020). Implicit linearization scheme for nonstandard two-phase flow in porous media. (external link)
• Marban, David Landa; Bødtker, Gunhild; Kumar, Kundan et al. (2020). An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube. (external link)
• Kumar, Kundan; List, Florian; Pop, Iuliu Sorin et al. (2020). Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. (external link)
• Marban, David Landa; Bødtker, Gunhild; Vik, Bartek Florczyk et al. (2020). Mathematical modeling, laboratory experiments, and sensitivity analysis of bioplug technology at Darcy scale. (external link)
• Ye, Ruichao; Kumar, Kundan; de Hoop, Maarten V. et al. (2020). A multi-rate iterative coupling scheme for simulating dynamic ruptures and seismic waves generation in the prestressed earth. (external link)
• Kassa, Abay; Gasda, Sarah; Kumar, Kundan et al. (2020). Impact of time-dependent wettability alteration on the dynamics of capillary pressure. (external link)
• Almani, Tameem; Manea, AM; Kumar, Kundan et al. (2019). Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. (external link)
• Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin et al. (2019). Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations. (external link)
• Landa-Marbán, David; Pop, Iuliu Sorin; Kumar, Kundan et al. (2019). Numerical Simulation of Biofilm Formation in a Microchannel. (external link)
• Storvik, Erlend; Both, Jakub; Kumar, Kundan et al. (2019). On the optimization of the fixed‐stress splitting for Biot's equations. (external link)
• Almani, T; Kumar, Kundan; Singh, G. et al. (2019). Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium. (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (2019). A singularity removal method for coupled 1D–3D flow models. (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin et al. (2019). Splitting method for elliptic equations with line sources. (external link)
• Landa-Marban, David; Liu, Na; Pop, Iuliu Sorin et al. (2018). A pore-scale model for permeable biofilm: Numerical simulations and laboratory experiments. (external link)
• Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin et al. (2018). Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. (external link)
• Borregales Reveron, Manuel Antonio; Kumar, Kundan; Radu, Florin Adrian et al. (2018). A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model. (external link)
• Endo Kokubun, Max Akira; Radu, Florin Adrian; Keilegavlen, Eirik et al. (2018). Transport of polymer particles in oil–water flow in porous media: Enhancing oil recovery. (external link)
• Borregales Reveron, Manuel Antonio; Radu, Florin Adrian; Kumar, Kundan et al. (2018). Robust iterative schemes for non-linear poromechanics. (external link)
• Bringedal, Carina; Kumar, Kundan (2017). Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow. (external link)
• Vasilyev, Leonid; Nordbotten, Jan Martin; Radu, Florin Adrian et al. (2017). On the Properties of the Parameter Space of the Generalized Continuum Transport Model for Description of Fluid Flow in Porous Networks. (external link)
• Both, Jakub; Borregales Reveron, Manuel Antonio; Kumar, Kundan et al. (2017). Robust fixed stress splitting for Biot's equations in heterogeneous media. (external link)
• Radu, Florin Adrian; Kumar, Kundan; Nordbotten, Jan Martin et al. (2017). A robust, mass conservative scheme for two-phase flow in porous media including Hoelder continuous nonlinearities. (external link)
• Almani, Tameem; Kumar, Kundan; Wheeler, M.F (2017). Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. (external link)
• Pop, Iuliu Sorin; Bogers, Jeroen; Kumar, Kundan (2017). Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition. (external link)
• Kumar, Kundan; Neuss-Radu, Maria; Pop, Iuliu Sorin (2016). Homogenization of a pore scale model for precipitation and dissolution in porous media. (external link)
• Almani, Tameem; Kumar, Kundan; Dogru, Ali H. et al. (2016). Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. (external link)
• Kumar, Kundan; Almani, Tameem; Singh, Gurpreet et al. (2016). Multirate undrained splitting for coupled flow and geomechanics in porous media. (external link)
• Girault, Vivette; Kumar, Kundan; Wheeler, Mary Fanett (2016). Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. (external link)
• Sepasian, Neda; Kumar, Kundan; Breeuwer, Marcel (2015). A geometrical approach to find corresponding patches in 3D medical surfaces. (external link)
• Radu, Adrian Florin; Nordbotten, Jan Martin; Pop, Iuliu Sorin et al. (2015). A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media. (external link)

Academic chapter/article/Conference paper

• Laguri, Vinod; Kumar, Kundan; Gupta, Pradeep et al. (2023). Thermodynamic analysis of a multi-evaporator refrigeration cycle using a two-phase ejector as an expansion device. (external link)
• Landa-Marbán, David; Kumar, Kundan; Tveit, Svenn et al. (2021). Numerical studies of CO2 leakage remediation by MICP-based plugging technology. (external link)
• Landa-Marbán, David; Kumar, Kundan; Gasda, Sarah Eileen et al. (2021). Numerical studies of long-term wettability alteration effects in CO2 storage applications. (external link)
• Kassa, Abay; Gasda, Sarah; Kumar, Kundan et al. (2018). Impact of Wettability Evolution on Dynamic Capillary Pressure. (external link)
• Kumar, Kundan; Ratnayake, R.M. Chandima (2017). Maintenance Regime Minimum (MRM): State of the Art — Maintaining Offshore Platforms Before Decommissioning. (external link)
• Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin et al. (2017). Iterative Methods for Coupled Flow and Geomechanics in Unsaturated Porous Media. (external link)

Documentary

• Nordbotten, Jan Martin; Kumar, Kundan; Keilegavlen, Eirik (2022). NFR Toppforsk project Thermo-Mechanical Energy Storage. (external link)

Academic lecture

• Gasda, Sarah Eileen; Landa-Marbán, David; Kassa, Abay et al. (2022). Modeling and Simulation of Wettability Alteration for CO2 Storage. (external link)
• Gasda, Sarah Eileen; Landa-Marbán, David; Kassa, Abay et al. (2022). Modeling and Simulation of Long-term Wettability Alteration on CO2 Storage Efficiency and Containment. (external link)
• Landa-Marbán, David; Tveit, Svenn; Gasda, Sarah Eileen et al. (2022). py-micp: An Open-Source Simulation Workflow for Field-Scale Application of Microbially Induced Calcite Precipitation Technology for Leakage Remediation. (external link)
• Landa-Marbán, David; Kumar, Kundan; Gasda, Sarah Eileen et al. (2021). Numerical studies of long-term wettability alteration effects in CO2 storage applications. (external link)
• Both, Jakub Wiktor; Kumar, Kundan; Nordbotten, Jan Martin et al. (2021). Robust block-partitioned solvers for flow in deformable porous media via alternating minimization. (external link)
• Kumar, Kundan (2021). Monotonicity of Effective Tensors with Respect to Geometric Perturbations. (external link)
• Kumar, Kundan (2021). Homogenization of Reactive Flows in Porous Media. (external link)
• Kumar, Kundan (2021). Using MRST for Solving Multiphase Flow Models in Porous Media. (external link)
• Kumar, Kundan (2021). Upscaling of flow models in a fractured media. (external link)
• Both, Jakub Wiktor; Kumar, Kundan; Nordbotten, Jan Martin et al. (2021). Block-partitioned solvers for poromechanics via gradient flows and minimization. (external link)
• Both, Jakub Wiktor; Kumar, Kundan; Nordbotten, Jan Martin et al. (2021). Robust block-partitioned solvers for poroelasticity derived from its gradient flow structures. (external link)
• Landa-Marbán, David; Tveit, Svenn; Kumar, Kundan et al. (2021). ad-micp: A third-party module for MRST to study CO2 leakage remediation by microbially induced calcite precipitation. (external link)
• Landa-Marbán, David; Tveit, Svenn; Kumar, Kundan et al. (2021). Numerical studies of microbially induced calcite precipitation at the field scale. (external link)
• Landa-Marbán, David; Kumar, Kundan; Tveit, Svenn et al. (2021). Numerical studies of CO2 leakage remediation by MICP-based plugging technology. (external link)
• Landa-Marbán, David; Tveit, Svenn; Kumar, Kundan et al. (2020). Modeling and Simulations of Microbially Induced Calcite Precipitation. (external link)
• Landa-Marbán, David; Bødtker, Gunhild; Vik, Bartek Florczyk et al. (2020). Numerical simulations of biofilms in core samples: MEOR and MICP. (external link)
• Both, Jakub; Kumar, Kundan; Nordbotten, Jan Martin et al. (2020). Robust Block-Partitioned Solvers for Poroviscoelasticity. (external link)
• Landa-Marbán, David; Liu, Na; Pop, Iuliu Sorin et al. (2019). Mathematical modelling of the bio-plug technology: laboratory experiments, upscaling, and numerical simulations. (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (2019). The mathematical structure of coupled 1D-3D flow models . (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (2019). Coupled 1D-3D flow models . (external link)
• Kassa, Abay; Gasda, Sarah; Kumar, Kundan et al. (2019). Constitutive relations modelling for dynamically altered porous medium. (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (2019). Analysis and approximation of coupled 1D-3D flow models. (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (2018). Well Modelling By Means Of Coupled 1D-3D Flow Models . (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan; Nordbotten, Jan Martin (2018). The Mathematical Structure of Coupled 1D-3D Models. (external link)
• Kassa, Abay; Gasda, Sarah; Kumar, Kundan et al. (2018). Impact of Wettability Evolution on Dynamic Capillary Pressure. (external link)
• Gasda, Sarah Eileen; Kassa, Abay; Radu, Florin Adrian et al. (2018). A Model for Dynamic Capillary Pressure with Time-Dependent Wettability Alteration. (external link)
• Kassa, Abay; Gasda, Sarah Eileen; Radu, Florin Adrian et al. (2018). Impact of Time-Dependent Wettability Alteration on Capillary Pressure. (external link)
• Landa-Marbán, David; Radu, Adrian Florin; Pop, Iuliu Sorin et al. (2017). An upscaled model for permeable biofilm formation in a thin strip. (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan (2017). Mixed methods for hierarchical flow models for wells in porous media . (external link)
• Gjerde, Ingeborg Gåseby; Kumar, Kundan (2017). Mixed methods for hierarchical flow models for wells in porous media . (external link)
• Kumar, Kundan (2017). Coupled Problems in Porous Media. (external link)
• Kumar, Kundan; Gjerde, Ingeborg Gåseby; Nordbotten, Jan Martin et al. (2017). Solution strategies for the coupling of mixed dimensional problems. (external link)
• Kumar, Kundan; Gjerde, Ingeborg Gåseby; Nordbotten, Jan Martin et al. (2017). Solution strategies for a 3D-1D coupling model. (external link)

Software

• Landa-Marbán, David; Tveit, Svenn; Kumar, Kundan et al. (2021). ad-micp: A module to study CO2 leakage remediation by microbially induced calcite precipitation (MICP). (external link)

Editorial

• Vermolen, Fred; Rodrigo, Carmen; Gaspar, Francisco José et al. (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. (external link)
• Radu, Florin Adrian; Kumar, Kundan; Berre, Inga et al. (2019). Preface. (external link)
• Salama, Amgad; Sun, Shuyu; El Amin, Mohamed F. et al. (2017). Flow and transport in porous media: a multiscale focus. (external link)

Doctoral dissertation

• Landa-Marbán, David; Radu, Florin Adrian; Kumar, Kundan et al. (2019). Mathematical modeling of microbial enhanced oil recovery with focus on bio-plug technology: from the pore to the core scale. (external link)

Academic anthology/Conference proceedings

• Radu, Florin Adrian; Kumar, Kundan; Berre, Inga et al. (2019). Numerical Mathematics and Advanced Applications ENUMATH 2017. (external link)

Abstract

• Kassa, Abay; Gasda, Sarah; Kumar, Kundan et al. (2018). Impact of time-dependent wettability alteration on dynamic capillary pressure. (external link)

Academic literature review

• Salama, Amgad; El Amin, Mohamed F.; Kumar, Kundan et al. (2017). Flow and transport in tight and shale formations: A review. (external link)

Report

• Radu, Florin Adrian; Kumar, Kundan; Nordbotten, Jan Martin et al. (2017). A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media. (external link)

Masters thesis

• Radu, Florin Adrian; Abay, Kassa; Kumar, Kundan (2016). Mathematical Modeling of Optimal Control Strategy for Microbial Enhanced Oil Recovery Processes. (external link)
• Radu, Florin Adrian; Samaneh, Mofrad Abolpour; Kumar, Kundan (2016). Microbially enhanced techniques for oil recovery and clogging.. (external link)

See a complete overview of publications in 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.