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Chemical kinetic models have become valuable tools for use in making both regulatory and business decisions. In industry, such models are increasingly being used to design reactors and chemical processes; and in public policy, these models have also been used in the implementation of the Montreal Protocol and the Clean Air Act.
Many exothermic chemical processes occur under spatially inhomogeneous conditions in which the chemical reactions are strongly coupled to heat and mass transfer processes. Simulation of first-principles models of turbulent flows alone is computationally demanding due to the nonlinearity in the partial differential equation describing conservation of momentum. Reacting flow simulations include an additional nonlinear partial differential equation for every chemical species being modeled. Nonlinearities, stiffness, and the sheer number of equations require model reduction techniques to make industrially relevant problems tractable by reducing the number of equations in the model while introducing an acceptable amount of error.
The goal of my dissertation is to advance these model reduction techniques so that first-principles models can enjoy widespread use as an engineering design tool. Supplementing existing numerical techniques for integrating partial differential equations (and ordinary differential equations) with an effective model reduction algorithm with rigorous error bounds can enhance our understanding of the physics behind the chemical processes driving technology today. Such techniques may also be applied to molecular dynamics simulations, economic models, and other situations in which large numbers of nonlinear differential equations are used to model dynamical systems.
Presentations:
1. G. Oxberry*, R.A. Handler, K.D. Housiadas and A.N. Beris, "Karhunen-Loève Analysis of Coherent Structures in Viscoelastic Turbulent Channel Flows." Paper presented at the 58th Annual Meeting of the Division of Fluid Dynamics -- (American Physical Society), Chicago, Illinois, November 20-22, 2005.
2. G. Samanta*, G. Oxberry, R.A. Handler, A.N. Beris and K.D. Housiadas, "Dynamic K-L analysis of coherent structures based on DNS of turbulent viscoelastic flows," Paper FM3 presented at: The Society of Rheology 78th Annual Meeting , October 8-12, 2006 - Portland, Maine.
3. G. Samanta, A.N. Beris, G. Oxberry, R.A. Handler and K.D. Housiadas*, "Dynamic K-L analysis of coherent strucures based on DNS of turbulent Newtonian and viscoelastic flows." Paper (A56) presented to the XVth International Workshop for Numerical Methods for Non-Newtonian Flows, Rhodes, Greece, June 6-10, 2007.
4. G. Samanta, A.N. Beris*, G. Oxberry, R.A. Handler and K.D. Housiadas, "Direct Numerical Simulation of Turbulent Viscoelastic Flows: Dynamic Karhunen-Loeve Analysis." Paper presented to the 6th International Congress on Industrial and Applied Mathematics (ICIAM '07), ETH, Zurich, Switzerland, July 16-20, 2007.
5. A. Mitsos, G. Oxberry*, P. I. Barton, W. H. Green, "Simultaneous Species and Reaction Elimination in Kinetic Mechanisms." Paper presented to International Workshop on Model Reduction in Reacting Flows, La Sapienza - Universita degli Studi, Rome, Italy, September 3-5, 2007.
6. G. Samanta*, A.N. Beris, G. Oxberry, R.A. Handler and K.D. Housiadas, "Dynamic K-L analysis of Coherent structures based on DNS of turbulent Newtonian and viscoelastic Flows", SIAM conference on Mathematics for Industry, Philadelphia, Pennsylvania, October 9-11, 2007.
7. A. Mitsos*, G. Oxberry, P. I. Barton, W. H. Green, "Kinetic Model Reduction By Simultaneous Reaction and Species Elimination." Paper presented to AIChE 2007 Annual Meeting, Salt Lake City, Utah, USA, November 4-9, 2007.
8. G. Samanta*, A.N. Beris, G. Oxberry, R.A. Handler and K.D. Housiadas, "Dynamic K-L analysis of coherent structures based on DNS of turbulent Newtonian and viscoelastic Flows." Paper presented to AIChE 2007 Annual Meeting, Salt Lake City, Utah, November 4-9 2007.
9. G. Samanta*, A.N. Beris, G. Oxberry, R.A. Handler and K.D. Housiadas, "Dynamic K-L analysis of coherent structures based on DNS of turbulent Newtonian and viscoelastic Flows". Paper presented to 60th Annual Meeting of APS-DFD, Salt Lake City, Utah, November 18-20, 2007.
10. G.M. Oxberry*, W.H. Green and P.I. Barton, "Affine lumping formalism for comparison of model reduction techniques." Paper presented to 2nd International Workshop on Model Reduction in Reacting Flows, South Bend, Indiana, March 30 - April 1, 2009.
11. G.M. Oxberry*, A. Mitsos, P.I. Barton, W.H. Green, "Range-constrained simultaneous reaction and species elimination in kinetic mechanisms." Paper presented to 2nd International Workshop on Model Reduction in Reacting Flows, South Bend, Indiana, March 30 - April 1, 2009.
12. G.M. Oxberry*, W.H. Green and P.I. Barton, "Affine lumping formalism for comparison of projection-based model reduction techniques." Paper presented to AIChE 2009 Annual Meeting, Nashville, Tennessee, November 8-13, 2009.
13. G.M. Oxberry*, A. Mitsos, P.I. Barton, W.H. Green, "Range-constrained simultaneous reaction and species elimination in kinetic mechanisms." Paper presented to AIChE 2009 Annual Meeting, Nashville, Tennessee, November 8-13, 2009.
Publications:
1. "Elucidation of the time scales of coherent structures in Newtonian turbulent channel flows through Karhunen-Loeve analysis" G. Oxberry, Masters thesis, University of Delaware, 2006.
2. "Time evolution K-L analysis of coherent structures based on DNS of turbulent Newtonian and viscoelastic flows" G. Samanta, G. M. Oxberry, A. N. Beris, R. A. Handler, and K. D. Housiadas. Journal of Turbulence, 9 (41) (2008), 1-25.
3. "Optimal automatic reaction and species elimination in kinetic mechanisms" A. Mitsos, G. M. Oxberry, P. I. Barton, and W. H. Green. Combustion and Flame, 155. (1-2), (2008), 118-132.
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