The broad area of research includes population dynamics of particulate processes. Particulate processes are well known in various branches of engineering including nano-technology, crystallization, precipitation, polymerization, aerosol, and emulsion processes. These processes are characterized by the presence of continuous phase and the dispersed phase composed of particles with a distribution of properties. The particles might be crystals, grains, drops or bubbles and may have several properties like size, composition, porosity and enthalpy etc. The particles may change their properties in a system due to several mechanisms like aggregation, breakage, nucleation, growth etc. As a result of particle formation mechanisms, particles change their properties and therefore a mathematical model named population balance is required to describe the changes of particle properties. There are several mathematical and numerical challenges to study such models. One of the current interests includes investigation of open problems in the theory of existence and uniqueness of its solution. We also develop and analysis numerical methods for solving these models. The current topics of research are:
Study inverse problems in population balances;
-Modelling of the aggregation and breakage kernels;
-Development of numerical methods for higher dimensional problems;
-Extending existence and uniqueness results for application oriented problems.
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On the approximate solutions of fragmentation equations Saha J., Kumar J. , Heinrich S. By Proceedings of the Royal Society A 474 - (2018)
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Development and convergence analysis of a finite volume scheme for solving breakage equation Kumar, J.; Saha, J.; Tsotsas, E. By SIAM Journal on Numerical Analysis 53 1672-1689 (2015)
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Numerical solutions for multidimensional fragmentation problems using finite volume methods Saha J., Das N. , Kumar J. , Bueck A. By Kinetic and Related Models 12 79-103 (2019)
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Convergence analysis of sectional methods for solving breakage population balance equations-II. The cell average technique Kumar, J.; Warnecke, G. By Numerische Mathematik 110 539-559 (2008)
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Convergence analysis of sectional methods for solving breakage population balance equations-I Kumar, J.; Warnecke, G. By Numerische Mathematik 111 81-108 (2008)
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A note on moment preservation of finite volume schemes for solving growth and aggregation population balance equations Kumar, J.; and Warnecke, G. By SIAM Journal of Scientific Computing 32 703-713 (2010)
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Moment preserving finite volume schemes for solving population balance equations incorporating aggregation, breakage, growth and source terms Kumar, R.; Kumar, J.; Warnecke, G. By Mathematical Models and Methods in Applied Science 23 1235-1273 (2013)
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Modeling of aggregation kernel using Monte Carlo simulations of spray fluidized bed agglomeration Hussain, M.; Kumar, J.; Tsotsas, E. By American Institute of Chemical Engineers (AIChE) Journal 60 855-868 (2014)
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An efficient numerical technique for the solution of nonlinear singular boundary value problems Singh , R.; Kumar, J. By Computer Physics Communications 185 1282-1289 (2014)
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The singular coagulation equation with multiple fragmentation Saha, J.; Kumar, J. By Journal of Applied Mathematics and Physics 66 919-941 (2015)
Co-Principal Investigator
- Development of Ultrahigh-Repetition-rate Soliton Light Sources based on High-quality Optical Waveguide Resonators Department of Science and Technology (International Bilateral Cooperation Division)
- Zonal Refinement Strategy to Expedite DEM Simulation of Fine Powder Flow AbbVie Inc.
- Zonal Refinement Strategy to Expedite DEM Simulation of Fine Powder Flow Eli Lill and Company
Ph. D. Students
Archita Karar
Area of Research: Mathematical Modelling and Simulations
Jayanta Paul
Area of Research: Numerical Mathematics
Mahto Lokeshwar Raghu
Area of Research: DEM Simulation
Niharika Mehra
Area of Research: Mathematical Modelling and Simulations
Priyanka
Area of Research: Mathematical Modelling and Numerical Analysis
