- E-mailKundan.Kumar@uib.no
- Phone+47 55 58 48 64+47 930 49 146
- Visitor AddressAllegaten 415007 BergenRoomRfg 4A16
- Postal AddressPostboks 78035020 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
- (2022). Field-scale impacts of long-term wettability alteration in geological CO<inf>2</inf> storage. International Journal of Greenhouse Gas Control.
- (2022). Convergence of single rate and multirate undrained split iterative schemes for a fractured biot model. Computational Geosciences.
- (2021). Practical approaches to study microbially induced calcite precipitation at the field scale. International Journal of Greenhouse Gas Control.
- (2021). Modeling of relative permeabilities including dynamic wettability transition zones. Journal of Petroleum Science and Engineering. 14 pages.
- (2021). Dimensional reduction of a fractured medium for a polymer EOR model. Computational Geosciences. 1753-1773.
- (2021). A Mixed Approach to the Poisson Problem with Line Sources. SIAM Journal on Numerical Analysis. 1117-1139.
- (2020). Rigorous upscaling of unsaturated flow in fractured porous media. SIAM Journal on Mathematical Analysis. 239-276.
- (2020). Mathematical modeling, laboratory experiments, and sensitivity analysis of bioplug technology at Darcy scale. SPE Journal. 3120-3137.
- (2020). Iterative solvers for Biot model under small and large deformations. Computational Geosciences.
- (2020). Implicit linearization scheme for nonstandard two-phase flow in porous media. International Journal for Numerical Methods in Fluids. 1-17.
- (2020). Impact of time-dependent wettability alteration on the dynamics of capillary pressure. Advances in Water Resources.
- (2020). Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem. Computers and Mathematics with Applications.
- (2020). Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. Journal of Computational Physics.
- (2020). Formal upscaling and numerical validation of unsaturated flow models in fractured porous media. Journal of Computational Physics. 21 pages.
- (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.
- (2020). An Upscaled Model for Permeable Biofilm in a Thin Channel and Tube. Transport in Porous Media. 83-112.
- (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.
- (2019). Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium. Computers and Mathematics with Applications. 1-18.
- (2019). Splitting method for elliptic equations with line sources. Mathematical Modelling and Numerical Analysis. 1715-1739.
- (2019). On the optimization of the fixed‐stress splitting for Biot's equations. International Journal for Numerical Methods in Engineering. 179-194.
- (2019). Numerical Simulation of Biofilm Formation in a Microchannel. Lecture Notes in Computational Science and Engineering. 799-807.
- (2019). Iterative Linearisation Schemes for Doubly Degenerate Parabolic Equations. Lecture Notes in Computational Science and Engineering. 49-63.
- (2019). Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences. 1-19.
- (2019). A singularity removal method for coupled 1D–3D flow models. Computational Geosciences.
- (2018). Transport of polymer particles in oil–water flow in porous media: Enhancing oil recovery. Transport in Porous Media. 1-19.
- (2018). Robust iterative schemes for non-linear poromechanics. Computational Geosciences. 1021-1038.
- (2018). Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers and Mathematics with Applications. 1479-1502.
- (2018). A pore-scale model for permeable biofilm: Numerical simulations and laboratory experiments. Transport in Porous Media. 643-660.
- (2018). A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model. Computers and Mathematics with Applications. 1466-1478.
- (2017). Robust fixed stress splitting for Biot's equations in heterogeneous media. Applied Mathematics Letters. 101-108.
- (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.
- (2017). Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow. Transport in Porous Media. 553-577.
- (2017). Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Computational Geosciences. 1157-1172.
- (2017). Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition. Vietnam Journal of Mathematics. 77-102.
- (2017). A robust, mass conservative scheme for two-phase flow in porous media including Hoelder continuous nonlinearities. IMA Journal of Numerical Analysis. 884-920.
- (2016). Multirate undrained splitting for coupled flow and geomechanics in porous media. Lecture Notes in Computational Science and Engineering. 431-440.
- (2016). Homogenization of a pore scale model for precipitation and dissolution in porous media. IMA Journal of Applied Mathematics. 877-897.
- (2016). Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. Computational Geosciences. 997-1011.
- (2016). Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Computer Methods in Applied Mechanics and Engineering. 180-207.
- (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.
- (2015). A geometrical approach to find corresponding patches in 3D medical surfaces. Lecture Notes in Computer Science (LNCS). 217-219.
Report
- (2017). A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media. .
Academic lecture
- (2021). ad-micp: A third-party module for MRST to study CO2 leakage remediation by microbially induced calcite precipitation.
- (2021). Using MRST for Solving Multiphase Flow Models in Porous Media.
- (2021). Upscaling of flow models in a fractured media.
- (2021). Robust block-partitioned solvers for poroelasticity derived from its gradient flow structures.
- (2021). Robust block-partitioned solvers for flow in deformable porous media via alternating minimization.
- (2021). Numerical studies of microbially induced calcite precipitation at the field scale.
- (2021). Numerical studies of long-term wettability alteration effects in CO2 storage applications.
- (2021). Numerical studies of CO2 leakage remediation by MICP-based plugging technology.
- (2021). Monotonicity of Effective Tensors with Respect to Geometric Perturbations.
- (2021). Homogenization of Reactive Flows in Porous Media.
- (2021). Block-partitioned solvers for poromechanics via gradient flows and minimization.
- (2020). Robust Block-Partitioned Solvers for Poroviscoelasticity.
- (2020). Numerical simulations of biofilms in core samples: MEOR and MICP.
- (2020). Modeling and Simulations of Microbially Induced Calcite Precipitation.
- (2019). The mathematical structure of coupled 1D-3D flow models .
- (2019). Mathematical modelling of the bio-plug technology: laboratory experiments, upscaling, and numerical simulations.
- (2019). Coupled 1D-3D flow models .
- (2019). Constitutive relations modelling for dynamically altered porous medium.
- (2019). Analysis and approximation of coupled 1D-3D flow models.
- (2018). Well Modelling By Means Of Coupled 1D-3D Flow Models .
- (2018). The Mathematical Structure of Coupled 1D-3D Models.
- (2018). Impact of Wettability Evolution on Dynamic Capillary Pressure.
- (2018). Impact of Time-Dependent Wettability Alteration on Capillary Pressure.
- (2018). A Model for Dynamic Capillary Pressure with Time-Dependent Wettability Alteration.
- (2017). Solution strategies for the coupling of mixed dimensional problems.
- (2017). Solution strategies for a 3D-1D coupling model.
- (2017). Mixed methods for hierarchical flow models for wells in porous media .
- (2017). Mixed methods for hierarchical flow models for wells in porous media .
- (2017). Coupled Problems in Porous Media.
- (2017). An upscaled model for permeable biofilm formation in a thin strip.
Editorial
- (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.
- (2019). Preface. Lecture Notes in Computational Science and Engineering. v-vi.
- (2017). Flow and transport in porous media: a multiscale focus. Geofluids. 1-3.
Academic anthology/Conference proceedings
- (2019). Numerical Mathematics and Advanced Applications ENUMATH 2017. Springer Berlin/Heidelberg.
Masters thesis
- (2016). Microbially enhanced techniques for oil recovery and clogging.
- (2016). Mathematical Modeling of Optimal Control Strategy for Microbial Enhanced Oil Recovery Processes.
Software
- (2021). ad-micp: A module to study CO2 leakage remediation by microbially induced calcite precipitation (MICP).
Doctoral dissertation
- (2019). Mathematical modeling of microbial enhanced oil recovery with focus on bio-plug technology: from the pore to the core scale.
Documentary
- (2022). NFR Toppforsk project Thermo-Mechanical Energy Storage.
Academic chapter/article/Conference paper
- (2021). Numerical studies of long-term wettability alteration effects in CO2 storage applications. 5 pages.
- (2021). Numerical studies of CO2 leakage remediation by MICP-based plugging technology. 7 pages.
- (2018). Impact of Wettability Evolution on Dynamic Capillary Pressure.
- (2017). Maintenance Regime Minimum (MRM): State of the Art — Maintaining Offshore Platforms Before Decommissioning. 10 pages.
- (2017). Iterative Methods for Coupled Flow and Geomechanics in Unsaturated Porous Media.
Abstract
- (2018). Impact of time-dependent wettability alteration on dynamic capillary pressure. EAGE Fifth CO2 Geological Storage Workshop.
Poster
- (2019). Constitutive relations for dynamic wettability transition zones.
- (2019). Biofilms in porous media: laboratory experiments, mathematical modeling and upscaling.
- (2018). Mathematical modelling of bacterial growth at different scales: numerical simulations and laboratory experiments.
- (2018). Mathematical modeling of biofilm formation: from the pore-scale to the core-scale.
- (2017). A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments.
Academic literature review
- (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).