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Averaging theories and multiscale methods (homogenization, volume averaging, termodynamically constrained averaging theory, numerical upscaling, computation of effective properties of composite materials)
Efficient numerical algorithms for multiphysics problems (domain decomposition, time splitting, multigrid, two-level preconditioners, Newton-Krylov-methods, stability analysis, a priori error estimates)
Mathematical modelling of flow and transport processes in porous media (porous-medium models with fluid-fluid interfacial area, sediment transport, mixed-dimensional models for fractured porous media)
Coupling free-flow and porous-medium systems (sharp interface, transition region, model validation and calibration, efficient numerical methods for coupled problems)
- C. T. Miller, W. G. Gray, C. E. Kees, I. Rybak, and B. J. Shepherd, “Correction to: Modelling Sediment Transport in Three-Phase Surface Water Systems,” J. Hydraul. Res., vol. 61, pp. 168–171, 2023, doi: 10.1080/00221686.2022.2107580.
- P. Strohbeck, E. Eggenweiler, and I. Rybak, “A modification of the Beavers-Joseph condition for arbitrary flows to the fluid-porous interface,” Transp. Porous Med., 2023, doi: 10.1007/s11242-023-01919-3.
- F. Mohammadi et al., “A Surrogate-Assisted Uncertainty-Aware Bayesian Validation Framework and its Application to Coupling Free Flow and Porous-Medium Flow,” Comput. Geosci. (submitted), 2022, [Online]. Available: https://arxiv.org/abs/2106.13639
- I. Kröker, S. Oladyshkin, and I. Rybak, “Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes-Darcy flow problems,” Comput. Geosci. (submitted), 2022, doi: 10.21203/rs.3.rs-1742793/v1.
- E. Eggenweiler, M. Discacciati, and I. Rybak, “Analysis of the Stokes-Darcy problem with generalised interface conditions,” ESAIM Math. Model. Numer. Anal., vol. 56, pp. 727–742, 2022, doi: 10.1051/m2an/2022025.
- E. Eggenweiler and I. Rybak, “Effective coupling conditions for arbitrary flows in Stokes-Darcy systems,” Multiscale Model. Simul., vol. 19, pp. 731–757, 2021, doi: 10.1137/20M1346638.
- A. Wagner et al., “Permeability estimation of regular porous structures: a benchmark for comparison of methods,” Transp. Porous Med., vol. 138, pp. 1–23, 2021, doi: 10.1007/s11242-021-01586-2.
- I. Rybak, C. Schwarzmeier, E. Eggenweiler, and U. Rüde, “Validation and calibration of coupled porous-medium and free-flow problems using pore-scale resolved models,” Comput. Geosci., vol. 25, pp. 621–635, 2021, doi: 10.1007/s10596-020-09994-x.
- I. Rybak and S. Metzger, “A dimensionally reduced Stokes-Darcy model for fluid flow in fractured porous media,” Appl. Math. Comp., vol. 384, 2020, doi: 10.1016/j.amc.2020.125260.
- E. Eggenweiler and I. Rybak, “Unsuitability of the Beavers-Joseph interface condition for filtration problems,” J. Fluid Mech., vol. 892, p. A10, 2020, doi: http://dx.doi.org/10.1017/jfm.2020.194.
- E. Eggenweiler and I. Rybak, “Interface conditions for arbitrary flows in coupled porous-medium and free-flow systems,” in Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 2020, vol. 323, pp. 345--353. doi: 10.1007/978-3-030-43651-3_31.
- C. T. Miller, W. G. Gray, C. E. Kees, I. V. Rybak, and B. J. Shepherd, “Modeling sediment transport in three-phase surface water systems,” J. Hydraul. Res., vol. 57, 2019, doi: 10.1080/00221686.2019.1581673.
- J. Magiera, C. Rohde, and I. Rybak, “A hyperbolic-elliptic model problem for coupled surface-subsurface flow,” Transp. Porous Media, vol. 114, pp. 425–455, 2016, doi: 10.1007/S11242-015-0548-Z.
- I. Rybak and J. Magiera, “Decoupled schemes for free flow and porous medium systems,” in Domain Decomposition Methods in Science and Engineering XXII, 2016, vol. 104, pp. 613--621. doi: 10.1007/978-3-319-18827-0\_54.
- I. Rybak, J. Magiera, R. Helmig, and C. Rohde, “Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems,” Comput. Geosci., vol. 19, pp. 299–309, Apr. 2015, doi: 10.1007/s10596-015-9469-8.
- I. V. Rybak, W. G. Gray, and C. T. Miller, “Modeling two-fluid-phase flow and species transport in porous media,” J. Hydrology, vol. 521, pp. 565--581, 2015, doi: https://doi.org/10.1016/j.jhydrol.2014.11.051.
- I. Rybak, “Coupling free flow and porous medium flow systems using sharp interface and transition region concepts,” in Finite Volumes for Complex Applications VII - Elliptic, Parabolic and Hyperbolic Problems, FVCA 7, Jun. 2014, vol. 78, pp. 703--711. doi: 10.1007/978-3-319-05591-6_70.
- I. Rybak and J. Magiera, “A multiple-time-step technique for coupled free flow and porous medium systems,” J. Comput. Phys., vol. 272, pp. 327--342, 2014, doi: 10.1016/j.jcp.2014.04.036.
- A. S. Jackson, I. Rybak, R. Helmig, W. G. Gray, and C. T. Miller, “Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 9. Transition region models,” Adv. Water Res., vol. 42, pp. 71--90, 2012, doi: 10.1016/j.advwatres.2012.01.006.
- K. Mosthaf et al., “A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow,” Water Resour. Res., vol. 47, p. W10522, 2011, doi: 10.1029/2011WR010685.
- R. Ewing, O. Iliev, R. Lazarov, I. Rybak, and J. Willems, “A simplified method for upscaling composite materials with high contrast of the conductivity,” SIAM J. Sci. Comp., vol. 31, no. 4, Art. no. 4, 2009, doi: 10.1137/080731906.
- O. Iliev and I. Rybak, “On numerical upscaling for flows in heterogeneous porous media,” Comput. Methods Appl. Math., vol. 8, no. 1, Art. no. 1, 2008.
- R. Ewing, O. Iliev, R. Lazarov, and I. Rybak, “On two-level preconditioners for flow in porous media,” Fraunhofer ITWM, 121, 2007.
- O. Iliev, I. Rybak, and J. Willems., “On upscaling heat conductivity for a class of industrial problems,” Fraunhofer ITWM, 120, 2007.
- O. Iliev and I. Rybak, “On approximation property of multipoint flux approximation method,” Fraunhofer ITWM, 119, 2007.
- O. Iliev and I. Rybak, “On numerical upscaling of flow in anisotropic porous media,” in Mathematisches Forschungsinstitut Oberwolfach Report No. 20, 2005, pp. 1162–1165.
- I. Rybak, “Monotone and conservative difference schemes for elliptic equations with mixed derivatives,” Math. Model. Anal., vol. 9, no. 2, Art. no. 2, 2004.
- I. Rybak, “Computational dynamics of shape memory alloys,” in Proc. of Lobachevski Mathematical Center, 2004, pp. 209--218.
- P. Matus and I. Rybak, “Difference schemes for elliptic equations with mixed derivatives,” Comput. Methods Appl. Math., vol. 4, no. 4, Art. no. 4, 2004.
- I. Rybak, “Monotone and conservative difference schemes for nonlinear nonstationary equations and equations with mixed derivatives,” Institute of Mathematics of the National Academy of Sciences of Belarus, 2004.
- I. Rybak, “Monotone difference schemes for equations with mixed derivatives in the case of boundary conditions of the third type,” Proceedings of the National Academy of Sciences of Belarus, Series of Physical-Mathematical Sciences, vol. 40, no. 1, Art. no. 1, 2004.
- I. Rybak, “Monotone and conservative difference schemes for equations with mixed derivatives,” Dokl. Akad. Navuk Belarusi, vol. 48, no. 1, Art. no. 1, 2004.
- P. Matus, R. Melnik, L. Wang, and I. Rybak, “Applications of fully conservative schemes in nonlinear thermoelasticity: modelling shape memory materials,” Math. Comp. Simulation, vol. 65, pp. 489--509, 2004.
- P. Matus and I. Rybak, “Monotone difference schemes for nonlinear parabolic equations,” Differential Equations, vol. 39, no. 7, Art. no. 7, 2003.
- I. Rybak, “Difference schemes for nonlinear models describing dynamic behaviour of shape memory alloys,” in Condensed State Physics: XI Republican Scientific Conference, Grodno, Belarus, April 23�25, 2003, 2003, pp. 200–203.
- R. Melnik, L. Wang, P. Matus, and I. Rybak, “Computational aspects of conservative difference schemes for shape memory alloys applications,” Lecture Notes in Comput. Sci., vol. 2668, pp. 791--800, 2003.
- P. Matus, R. Melnik, and I. Rybak, “Fully conservative difference schemes for nonlinear models describing dynamics of materials with shape memory,” Dokl. Akad. Navuk Belarusi, 47(1):15–17, 2003., vol. 47, no. 1, Art. no. 1, 2003.
Habilitation in Mathematics (University of Stuttgart, Germany)
|Nov. 2001 -- Nov. 2004||
PhD in Physics and Mathematics (Institute of Mathematics, National Academy of Sciences of Belarus)
|Sep. 1996 -- Jun. 2001||MSc in Applied Mathematics (Belarusian State University)|
|Apr. 2000 -- Jun. 2001||MSc in Economical Cybernetics (Belarusian State University)|
|2022-2025||Principal investigator in ANR-DFG Project FLUPOR: "Generalised Interface Conditions for Multi-Dimensional Inertial Flows in Fluid-Porous Systems" with Philippe Angot, Aix-Marseille Université (1 postdoc position for 24 months, 2 PhD positions for 36 months)|
|2022-2025||Principal investigator in Collaborative Research Centre (SFB) 1313 "Interface-Driven Multi-Field Processes in Porous Media – Flow, Transport and Deformation'' (Phase 2), German Research Foundation (DFG), Project A03 "Development of interface concepts using averaging techniques" (1 PhD position for 48 months)|
|2018-2021||Principal investigator in Collaborative Research Centre (SFB) 1313 "Interface-Driven Multi-Field Processes in Porous Media – Flow, Transport and Deformation'', German Research Foundation (DFG), Project A03 "Development of interface concepts using averaging techniques"|
|2016-2017||Eigene Stelle, ``Mathematische Modellierung und Numerik von Übergangsbereichen zwischen porösen Medien und freien Strömungen'', DFG Projekt, RY 126/2-2|
|2012-2015||Eigene Stelle, ``Mathematische Modellierung und Numerik von Übergangsbereichen zwischen porösen Medien und freien Strömungen'', DFG Projekt, RY 126/2-1|
|2007-2009||Project participant, ``Development of multilevel algorithms for simulation of fluid flows in porous media'', Belarusian Republican Foundation for Fundamental Research, F07MS-054|
|2004-2007||Project participant, ``Hydrogeological and geo-environmental simulations: a contribution to the algorithms and advanced applications'', INTAS-03-50-4395|
|2004-2006||Principal investigator, ``Development of monotone and conservative difference schemes for problems of mathematical physics with mixed derivatives'', Belarusian Republican Foundation for Fundamental Research, F04M-136|
- Advances in Computational Mathematics
- Advances in Water Resources (Certificate of Excellence in Reviewing, 2013)
- Applied Mathematics and Computation
- Applied Mathematical Modelling
- Applied Numerical Mathematics
- Computational and Applied Mathematics
- Computational Geosciences
- Computers and Mathematics with Applications
- Computer Methods in Applied Mechanics and Engineering
- IMA Journal of Numerical Analysis
- International Journal of Heat and Mass Transfer
- Journal of Computational and Applied Mathematics
- Journal of Computational Physics
- Journal of Hydraulic Research
- Journal of Hydrology
- Journal of Porous Media
- Journal of Scientific Computing
- Mathematics of Computation
- Mathematical Reviews
- Numerical Methods for Partial Differential Equations
- SIAM Journal on Numerical Analysis
- Transport in Porous Media
- Water Resources Research
Joscha Nickl (Aix-Marseille-Université)
- L. Ruan: Generalised interface conditions for multi-dimensional inertial
flows in fluid-porous systems, since May 2022
- U. Ghani: Dimensionally reduced models for fluid flow and species transport in surface-groundwater systems (DAAD scholarship), since December 2021
- E. Eggenweiler: Interface conditions for arbitrary flows in Stokes-Darcy systems: derivation, analysis and validation, since June 2018
- P. Strohbeck: Development of interface concepts using averaging techniques
since November 2022
- S. Kahle: Data-driven homogenization and boundary layer theory based on neural networks, 2023
- M. Wolf: Data-driven homogenization for two-phase flows in porous media, 2023
- P. Strohbeck: Efficient preconditioners for Stokes-Darcy problems with
generalized interface conditions, 2022
- N. Nutsch: Optical flow methods for fluid velocity reconstruction in
fractured porous media, 2022
- J. Nickl: Generalised interface conditions for Stokes–Darcy problems
with symmetric stress tensor, 2021
- A. Baric: Boundary layers for coupled problems in porous media, 2019
- Y. Öztürk: Upscaling of capillary network structures, 2018
- F. Castor: Preconditioners for saddle point problems in fluid dynamics, 2021
- S. Kahle: Stochastic gradient descent for image registration, 2021
- M. Wolf: Data-driven homogenization based on neural networks for permeability estimation, 2020
- P. Strohbeck: Optimization of sharp interface location for coupled porous-medium and free-flow systems, 2020
- N. Nutsch: Numerical optimization methods for image registration with mutual information, 2020
- A.-K. Kapfenstein: Numerical optimization algorithms for image registration, 2020
- J. Flad: Image Registration using Mutual Information, 2019
- T. Schwaderer: Krylov subspace methods for diffusion equations with
discontinuous coefficients, 2019
- L. Ruan: Newton-Krylov Methods for Porous Media Flows, 2019
- A. Savanovic: Efficient numerical methods for ill-conditioned linear
- L. Igel: Numerical methods for equilibrium and kinetic models, 2018
- D. Beyer: Newton-Krylov methods for unsaturated flows in porous media, 2018
- S. Özkan: Homogenisation of flow and transport in porous media, 2018
- S. Matskevich: Mathematical modelling of filtration processes, 2018
- E. Eggenweiler: Mathematical modelling of flows in fractured porous media,
- A. Baric: Mathematical modelling of coupled free and subsurface water