### Research Interests

Dr. Fomin's research interests are: mathematical modeling of dispersion, convection and reaction in porous media in application to contaminant hydrology and bioremediation.; mathematical modeling of tsunami wave dynamics based on the “shallow water” non-linear partial differential equations; and mathematical modeling of Non-Newtonian films in application to coating technology and polymer molding.

### Research Projects

PI’s: Sergei Fomin

Title: Research Experiences in Mathematics for Undergraduates and Teachers

Funding Agency: NSF

Dates: 2012-2015

Award Amount: *$339,600*

### Related Publications

**Book:**

Sergei Fomin and Vladimir Chugunov “*Mathematical Modeling of Mass Transport in Complex Media”*, COE Lecture Series, Vol. 7, Tohoku University Press, Sendai, Japan, **2007**, pp. 1-218.

**Journal papers and book chapters (since 2001) **

S. Fomin, J., Watterson, S. Raghunathan and E. Harkin-Jones, “The Run-Off Condition for Rimming Flow of a Power-Law Fluid*”, Theoretical and Computational Fluid Dynamics*, Vol.15, No.2, **2001**, pp. 83-94.

S. Fomin and A. Wilchinsky, “Shape-Factor Effect on Melting within an Elliptic Capsule”, *International Journal of Heat and Mass Transfer*, Vol. 45, No. 14, **2002**, pp. 3045-3054.

A. Wilchinsky, S. Fomin and T. Hashida, “Contact Melting Inside an Elastic Capsule”, *International Journal of Heat and Mass Transfer*, Vol. 45, No. 20, **2002**, pp. 4097-4106.

S.A. Fomin, and V.A. Chugunov, "Optimal Distribution of a Heat Source Within a Thermopenetrator", *Engineering Analysis with Boundary Elements,* Vol. 26, No. 7, **2002**, pp. 613-620.

S. Fomin, J., Watterson, S. Raghunathan and E. Harkin-Jones, “Steady-State Rimming Flow of the Generalized Newtonian Fluid”, *Physics of Fluids,* Vol.14, No. 9, **2002,** pp. 3350-3353.

S. Fomin, V. Chugunov, T. Hashida, S. Saito and Y. Suto, “Heat Flux on the Bore-Face and Temperature Distribution in the Formation”, *GRC Transactions*, Vol. 26, **2002**, pp.803-807.

S. Fomin, K. Yoshida and T. Hashida, “Analysis of Thermal Effectiveness of Geothermal Multi-Borehole Circulating System”, *GRC Transactions*, Vol. 26, **2002**, pp.279-283.

S. Fomin, T. Hashida and J. Watterson, “Fundamentals of the Rimming Flows of the Non-Newtonian Fluids”, *Journal of Non-Newtonian Fluid Mechanics*, Vol. 111, **2003**, pp.19-40.

V. Chugunov, S. Fomin, and T. Hashida, “Heat Flow Rate at a Bore-Face and Temperature in the Surrounding a Borehole Non-Homogeneous Media”, *Int. Journal of Heat and Mass Transfer*, Vol. 46, **2003**, pp. 4769-4778.

S. Fomin, T. Hashida, A. Shimizu, K. Matsuki and K. Sakaguchi, “Fractal Concept in Numerical Simulation of Hydraulic Fracturing of the Hot Dry Rock Geothermal Reservoir”, *Hydrological Processes*, Vol. 17, **2003**, pp.2975-2989.

S. Fomin, V. Chugunov and T. Hashida, “Analytical modeling of the formation temperature stabilization during the borehole shut-in period”, *Geophysical Journal International*, Vol. 155, **2003**, pp.469-478.

K. Yoshida, A. Shimizu, S. Fomin and T. Hashida “Computer simulation of fluid flow in fractured media. The effect of thermal dispersion”, in *Non-destructive Testing and Computer Simulations in Science and Engineering**,* SPIE Proceedings Series, Vol. 5127*,***2003**, pp. 207-215.

S. Fomin, A. Shimizu, K. Matsuki, K. Sakaguchi and T. Hashida, “Simulation of the fracture shear dilation”, in *Non-destructive Testing and Computer Simulations in Science and Engineering**,* SPIE Proceedings Series, Vol. 5127*,***2003**, pp. 216-221.

S. Fomin, A. Shimizu and T. Hashida, “ Numerical Simulation of the Fracture Type Reservoir Growth”, *Strength, Fracture and Complexity*, Vol. 1(2), **200****3,** IOS Press, pp. 69-77.

K. Yoshida, S. Fomin and T. Hashida, “Numerical Simulation of the Large-Scale Geothermal Reservoir with Multiple-Borehole-Circulation System”, *GRC Transactions*, Vol. 27, **2003,** pp. 747-751.

S. Fomin, Z. Jing and T. Hashida, “The effect of thermal, chemical, hydrological and mechanical factors on water/rock interaction in HDR geothermal systems”. In: O Stephansson, J. A. Hudson and L. Jing (eds.), Coupled thermo-hydro-mechanical-chemical processes in geo-systems: fundamentals, modeling, experiments and applications. Elsevier Geo-Engineering Book Series, Volume 2, **2004**, Elsevier, Oxford. p.649-654.

S. Fomin, V. Chugunov and T. Hashida, “Mathematical modelling of borehole grouting in permafrost”. In: O. Stephansson, J. A. Hudson and L. Jing (eds.), Coupled thermo-hydro-mechanical-chemical processes in geo-systems: fundamentals, modeling, experiments and applications. Elsevier Geo-Engineering Book Series, Volume 2, **2004**, Elsevier, Oxford. p.773-778.

S. Fomin and T. Hashida “Advances in mathematical modelling of hydraulic stimulation of a subterranean fractured reservoir”, in *Non-destructive Testing and Computer Simulations in Science and Engineering**,* SPIE Proceedings Series, Vol. 5831*,***2005**, pp. 148-154.

S. Fomin, T. Hashida, V. Chugunov and A.V. Kuznetsov, “A borehole temperature during drilling in a fractured rock formation”, *Int. Journal of Heat and Mass Transfer*, vol. 48, **2005**, pp. 385-394.

S. Fomin, V. Chugunov and T. Hashida, “The effect of non-Fickian diffusion into surrounding rocks on contaminant transport in fractured porous aquifer”, *Proceedings of Royal Society A*, vol. 461 **2005**, pp. 2923-2939.

K. Yoshida, S. Fomin and T. Hashida, “Numerical analysis for unsteady-state growth behavior of hydraulically induced reservoirs”, *GRC Transactions*, Vol. 29, **2005,** pp. 197-200.

S. Fomin, “Three Regimes of Non-Newtonian Rimming Flow”, *ASME Journal of Fluids Engineering*, v. 128, **2006**, 107-112.

S. Fomin, V. Chugunov and T. Hashida, “Assessment of Stimulated Area Growth During High-Pressure Stimulation of Fractured Subsurface Reservoir”, *Transport in Porous Media, vol. 63, 2006, pp. 99–125.*

S. Fomin, V. Chugunov and T. Hashida , “Simulation of contaminant transport in a fractured porous aquifer”, *Journal of Fluids Engineering*, vol.129, **2007**, pp.1157-1163.

T. Hashida, R. Chiba, S. Fomin “*Mega-Scale Fluid Flow in Complex Subsurface Fracture Systems”*, COE Lecture Series, Vol. 9, Chapter 7, Tohoku University Press, Sendai, Japan, **2008**, pp. 241-261.

Ryuichi Chiba, Takashi Okaze, Sergei Fomin, Vladimir Chugunov, Yuichi Niibori, Hisao Fukunaga, and Toshiyuki Hashida, “ Numerical Simulations of the Anomalous Solute Transport in a Fractured Porous Aquifer”, *GRC Transactions, Vol. 32, 2008, pp. 441-443.*

Ana Suzuki, Ryuichi Chiba, Takashi Okaze, Yuichi Niibori, Hisao Fukunaga, Sergei Fomin, Vladimir Chugunov, and Toshiyuki Hashida, “ Characterizing non_Fickian Transport in Fractured Rock Masses Using Fractional Derivative-Based Method”, *GRC Transactions*, Vol. 34, **2010**, pp. 1179-1184.

S. Fomin, V. Chugunov, T. Hashida, "Application of Fractional Differential Equations for Modeling the Anomalous Diffusion of Contaminant from Fracture into Porous Rock Matrix with Bordering Alteration Zone", *Transport in Porous Media*, vol. 81, **2010**, pp.187–205.

S. Fomin, K. Kilpatrick, and R. Hubbard, “Rimming Flow of a Power-Law Fluid: Qualitative Analysis of the Mathematical Model and Analytical Solutions” *Applied Mathematics and Computation*, vol. 216, **2010,** pp. 2169–2176.

S. Fomin, J. Debrunner, A. Mazurenko, and B. Nelson, “Steady State Visco-Elastic Rimming Flow”, *Applied Mathematical Modeling*, vol.35, **2011,** pp.1846–1860.

Sergei A. Fomin, Vladimir A. Chugunov, Toshiyuki Hashida, “Non-Fickian mass transport in fractured porous media” *Advances in Water Resources*, vol. 34, **2011**, pp. 205–214.

S. Fomin, V. Chugunov and T. Hashida, "Mathematical modeling of Anomalous Diffusion in Porous Media", *Fractional Differential Calculus*, **2011**, vol.1, pp. 1-28.

Anna Suzuki, Hiroshi Makita, Yuichi Niibori, Sergei A. Fomin, Vladimir A. Chugunov, Toshiyuki Hashida, “Characterization of Tracer Responses Using Fractional Derivative –Based Mathematical Model and Its Application to Prediction of Mass Transport in Fractured Reservoirs*”, GRC Transactions*, Vol. 36, **2012**, pp. 1391-1396.

S. Fomin, A. Mazurenko, R. Shankar and V. Chugunov, “Reactive Rimming Flow of Non-Newtonian Fluids”, *Applied Mathematics and Computation*, 2013, accepted (in press).

### Research Areas

Energy, Engineering, Water