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. 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

Finite Element Analysis, Fall 2015, Fall 2017, Fall 2022, Fall 2025

Flow in Porous Media, Fall 2024

Continuum Mechanics, Spring 2020, Spring 2021, Spring 2022, Spring 2023

Numerical Linear Algebra, Fall 2020, Fall 2021

Computational Science II, Spring 2015, Spring 2016, Spring 2017, Spring 2018

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

Ordinary Differential Equations, Fall 2018,

Advanced Linear Algebra, Spring 2019,

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.

Vitenskapelig bokkapittel

• Jakob Seierstad Stokke; Morten Jakobsen; Kundan Kumar et al. (2025). A History-Dependent Dynamic Biot Model. (ekstern lenke)
• Vinod Laguri; Kundan Kumar; Pradeep Gupta et al. (2023). Thermodynamic analysis of a multi-evaporator refrigeration cycle using a two-phase ejector as an expansion device. (ekstern lenke)
• David Landa-Marbán; Kundan Kumar; Sarah Eileen Gasda et al. (2021). Numerical studies of long-term wettability alteration effects in CO2 storage applications. (ekstern lenke)
• David Landa-Marbán; Kundan Kumar; Svenn Tveit et al. (2021). Numerical studies of CO2 leakage remediation by MICP-based plugging technology. (ekstern lenke)
• Jakub Both; Kundan Kumar; Jan Martin Nordbotten et al. (2017). Iterative Methods for Coupled Flow and Geomechanics in Unsaturated Porous Media. (ekstern lenke)
• Kundan Kumar; R.M. Chandima Ratnayake (2017). Maintenance Regime Minimum (MRM): State of the Art — Maintaining Offshore Platforms Before Decommissioning. (ekstern lenke)
• Abay Kassa; Sarah Gasda; Kundan Kumar et al. (2018). Impact of Wettability Evolution on Dynamic Capillary Pressure. (ekstern lenke)

Konferanseforedrag

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

Konferanseposter

• David Landa-Marbán; Na Liu; Iuliu Sorin Pop et al. (2018). Mathematical modeling of biofilm formation: from the pore-scale to the core-scale. (ekstern lenke)
• David Landa-Marbán; Na Liu; Iuliu Sorin Pop et al. (2019). Biofilms in porous media: laboratory experiments, mathematical modeling and upscaling. (ekstern lenke)
• David Landa-Marbán; Na Liu; Sorin Iuliu Pop et al. (2018). Mathematical modelling of bacterial growth at different scales: numerical simulations and laboratory experiments. (ekstern lenke)
• Hasan Gürsel; Geir Ersland; Sarah Eileen Gasda et al. (2025). Modeling the Temporal Dynamics of Formation Damage during Produced Water Re-injection. (ekstern lenke)
• Abay Kassa; Sarah Gasda; Kundan Kumar et al. (2019). Constitutive relations for dynamic wettability transition zones. (ekstern lenke)
• David Landa-Marbán; Na Liu; Iuliu Sorin Pop et al. (2017). A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments. (ekstern lenke)
• Hasan Gürsel; Geir Ersland; Sarah Eileen Gasda et al. (2024). Modeling the Temporal Dynamics of Formation Damage during Produced Water Re-injection. (ekstern lenke)
• Geir Ersland; Sarah Eileen Gasda; Kundan Kumar (2024). Modeling the Temporal Dynamics of Formation Damage during Produced Water Re-injection. (ekstern lenke)
• Hasan Gürsel; Geir Ersland; Sarah Eileen Gasda et al. (2024). Modeling the Temporal Dynamics of Formation Damage during Produced Water Re-injection. (ekstern lenke)

Masteroppgave

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

Vitenskapelig artikkel

• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten et al. (2019). Splitting method for elliptic equations with line sources. (ekstern lenke)
• Manuel Antonio Borregales Reveron; Kundan Kumar; Florin Adrian Radu et al. (2018). A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model. (ekstern lenke)
• David Landa-Marbán; Svenn Tveit; Kundan Kumar et al. (2021). Practical approaches to study microbially induced calcite precipitation at the field scale. (ekstern lenke)
• Leonid Vasilyev; Jan Martin Nordbotten; Florin Adrian Radu et al. (2017). On the Properties of the Parameter Space of the Generalized Continuum Transport Model for Description of Fluid Flow in Porous Networks. (ekstern lenke)
• Carina Bringedal; Kundan Kumar (2017). Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow. (ekstern lenke)
• Adrian Florin Radu; Iuliu Sorin Pop; Florian List et al. (2020). Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. (ekstern lenke)
• Jakub Both; Kundan Kumar; Jan Martin Nordbotten et al. (2019). Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations. (ekstern lenke)
• Abay Kassa; Kundan Kumar; Sarah Gasda et al. (2020). Implicit linearization scheme for nonstandard two-phase flow in porous media. (ekstern lenke)
• Ruichao Ye; Kundan Kumar; Maarten V. de Hoop et al. (2020). A multi-rate iterative coupling scheme for simulating dynamic ruptures and seismic waves generation in the prestressed earth. (ekstern lenke)
• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten (2019). A singularity removal method for coupled 1D–3D flow models. (ekstern lenke)
• David Landa-Marban; Na Liu; Iuliu Sorin Pop et al. (2018). A pore-scale model for permeable biofilm: Numerical simulations and laboratory experiments. (ekstern lenke)
• Florin Adrian Radu; Kundan Kumar; Jan Martin Nordbotten et al. (2017). A robust, mass conservative scheme for two-phase flow in porous media including Hoelder continuous nonlinearities. (ekstern lenke)
• Abay Kassa; Sarah Eileen Gasda; David Landa-Marbán et al. (2022). Field-scale impacts of long-term wettability alteration in geological CO2 storage. (ekstern lenke)
• Manuel Antonio Borregales Reveron; Kundan Kumar; Jan Martin Nordbotten et al. (2020). Iterative solvers for Biot model under small and large deformations. (ekstern lenke)
• Tameem Almani; Kundan Kumar; Ali H. Dogru et al. (2016). Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. (ekstern lenke)
• Tameem Almani; AM Manea; Kundan Kumar et al. (2019). Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. (ekstern lenke)
• Erlend Storvik; Jakub Both; Kundan Kumar et al. (2019). On the optimization of the fixed‐stress splitting for Biot's equations. (ekstern lenke)
• Kundan Kumar; Svetlana Kyas; Jan Martin Nordbotten et al. (2020). Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem. (ekstern lenke)
• Jakub Both; Manuel Antonio Borregales Reveron; Kundan Kumar et al. (2017). Robust fixed stress splitting for Biot's equations in heterogeneous media. (ekstern lenke)
• Tameem Almani; Kundan Kumar; Mary F. Wheeler (2023). Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media. (ekstern lenke)
• David Landa-Marbán; Iuliu Sorin Pop; Kundan Kumar et al. (2019). Numerical Simulation of Biofilm Formation in a Microchannel. (ekstern lenke)
• Martin Sandanger Dugstad; Kundan Kumar; Øystein Pettersen (2021). Dimensional reduction of a fractured medium for a polymer EOR model. (ekstern lenke)
• T. Almani; Kundan Kumar (2022). Convergence of single rate and multirate undrained split iterative schemes for a fractured biot model. (ekstern lenke)
• Abay Kassa; Sarah Gasda; Kundan Kumar et al. (2020). Impact of time-dependent wettability alteration on the dynamics of capillary pressure. (ekstern lenke)
• Neda Sepasian; Kundan Kumar; Marcel Breeuwer (2015). A geometrical approach to find corresponding patches in 3D medical surfaces. (ekstern lenke)
• David Landa Marban; Gunhild Bødtker; Kundan Kumar et al. (2020). An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube. (ekstern lenke)
• T. Almani; Kundan Kumar (2024). Convergence of multirate fixed stress split iterative schemes for a fractured Biot model. (ekstern lenke)
• Kundan Kumar; Tameem Almani; Gurpreet Singh et al. (2016). Multirate undrained splitting for coupled flow and geomechanics in porous media. (ekstern lenke)
• Iuliu Sorin Pop; Jeroen Bogers; Kundan Kumar (2017). Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition. (ekstern lenke)
• Vivette Girault; Kundan Kumar; Mary Fanett Wheeler (2016). Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. (ekstern lenke)
• Kundan Kumar; Maria Neuss-Radu; Iuliu Sorin Pop (2016). Homogenization of a pore scale model for precipitation and dissolution in porous media. (ekstern lenke)
• Florian List; Kundan Kumar; Iuliu Sorin Pop et al. (2020). Rigorous upscaling of unsaturated flow in fractured porous media. (ekstern lenke)
• David Landa Marban; Gunhild Bødtker; Bartek Florczyk Vik et al. (2020). Mathematical modeling, laboratory experiments, and sensitivity analysis of bioplug technology at Darcy scale. (ekstern lenke)
• Ingeborg Gåseby Gjerde; Kundan Kumar; Jan Martin Nordbotten (2021). A Mixed Approach to the Poisson Problem with Line Sources. (ekstern lenke)
• Manuel Antonio Borregales Reveron; Florin Adrian Radu; Kundan Kumar et al. (2018). Robust iterative schemes for non-linear poromechanics. (ekstern lenke)
• Shridhar Kumar; Pratibhamoy Das; Kundan Kumar (2024). Adaptive mesh based efficient approximations for Darcy scale precipitation–dissolution models in porous media. (ekstern lenke)
• Tameem Almani; Kundan Kumar; M.F Wheeler (2017). Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. (ekstern lenke)
• Adrian Florin Radu; Jan Martin Nordbotten; Iuliu Sorin Pop et al. (2015). A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media. (ekstern lenke)
• Nadia Skoglund Taki; Kundan Kumar (2024). Well-posedness of evolutionary differential variational–hemivariational inequalities and applications to frictional contact mechanics. (ekstern lenke)
• T Almani; Kundan Kumar; G. Singh et al. (2019). Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium. (ekstern lenke)
• Maarten V. de Hoop; Kundan Kumar; Ruichao Ye (2020). Analysis of dynamic ruptures generating seismic waves in a self-gravitating planet: An iterative coupling scheme and well-posedness. (ekstern lenke)
• Jakub Both; Kundan Kumar; Jan Martin Nordbotten et al. (2018). Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. (ekstern lenke)
• Johannes Kraus; Kundan Kumar; Maria Lymbery et al. (2024). A fixed-stress splitting method for nonlinear poroelasticity. (ekstern lenke)
• Abay Kassa; Sarah E. Gasda; Kundan Kumar et al. (2021). Modeling of relative permeabilities including dynamic wettability transition zones. (ekstern lenke)
• Kundan Kumar; Florian List; Iuliu Sorin Pop et al. (2020). Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. (ekstern lenke)
• Martin Sandanger Dugstad; Kundan Kumar (2022). Dimensional reduction of a fractured medium for a two-phase flow. (ekstern lenke)
• Max Akira Endo Kokubun; Florin Adrian Radu; Eirik Keilegavlen et al. (2018). Transport of polymer particles in oil–water flow in porous media: Enhancing oil recovery. (ekstern lenke)

Konferanseabstrakt

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

Lederartikkel

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

Antologi

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

Forskningsrapport

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

Doktorgradsavhandling

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

Vitenskapelig litteraturgjennomgang

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

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