Artificial Intelligence–Assisted Reduced-Order Modeling and Stability Control in Granular Couette Flow

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Year : 2026 | Volume : 13 | 03 | Page :
By

Lakshmi. N. Sridhar,

  1. Professor, Chemical Engineering Department, University of Puerto Rico, Mayaguez, Puerto Rico, United States

Abstract

This study develops a reduced-order and stability-aware modeling framework for dense granular Couette flow by integrating continuum mechanics, bifurcation analysis, and data-driven stability estimation. Starting from coupled governing equations for momentum, granular temperature, and microstructural evolution, the system is nondimensionalized and reduced using a Galerkin projection consistent with shear-driven boundary conditions. This yields a low-dimensional nonlinear dynamical system that preserves the essential coupling between velocity, fluctuation energy, and structural relaxation. A fast–slow decomposition is then used to eliminate the granular temperature dynamics, resulting in an effective nonlinear feedback formulation in which structural evolution modifies the apparent viscosity. The reduced system exhibits a Hopf bifurcation, leading to self-sustained oscillations arising from delayed interaction between shear production, dissipation, and structural rearrangement. To incorporate stability into optimal control, a neural network surrogate is trained to approximate the dominant eigenvalue of the linearized system, providing a smooth and differentiable stability indicator. This surrogate is embedded into a soft penalty formulation within a Pyomo.DAE-based optimal control framework. Results show that unconstrained optimization drives the system toward the vicinity of the Hopf bifurcation, achieving improved performance but inducing oscillatory dynamics. When stability constraints are enforced, the optimal trajectory shifts away from the instability boundary, yielding a slightly higher but dynamically stable solution. These results demonstrate a fundamental trade-off between optimality and stability in granular Couette flow and highlight the effectiveness of surrogate-based stability control in nonlinear fluid systems.

Keywords: Granular Couette flow, Hopf Bifurcation, Optimal Control, Artificial Intelligence, Limit Cycle

How to cite this article: Lakshmi. N. Sridhar. Artificial Intelligence–Assisted Reduced-Order Modeling and Stability Control in Granular Couette Flow. Emerging Trends in Chemical Engineering. 2026; 13(03):-.
How to cite this URL: Lakshmi. N. Sridhar. Artificial Intelligence–Assisted Reduced-Order Modeling and Stability Control in Granular Couette Flow. Emerging Trends in Chemical Engineering. 2026; 13(03):-. Available from: https://journals.stmjournals.com/etce/article=2026/view=252205

References

  1. Savage SB. Granular flows down rough inclines. Adv Appl Mech. 1982;24:289–366.
  2. Jenkins JT, Savage SB. A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J Fluid Mech. 1983;130:187–202.
  3. Lun CKK, Savage SB, Jeffrey DJ, Chepurniy N. Kinetic theories for granular flow: Inelastic particles in Couette flow. J Fluid Mech. 1984;140:223–256.
  4. Jenkins JT, Richman MW. Kinetic theory for plane flows of identical, smooth, inelastic spheres. Phys Fluids. 1985;28:3485–3494.
  5. Savage SB. Flow of granular materials in shear. J Fluid Mech. 1989;203:449–473.
  6. Richman MW. Boundary conditions for granular flows. Z Angew Math Phys. 1988;39:837–848.
  7. Nott PR, Mohan LS, Rao KK. A frictional Cosserat model for granular flow in a vertical channel. J Fluid Mech. 1999;397:203–229.
  8. Nott PR, Alam M, Agrawal K, Jackson R, Sundaresan S. The effect of boundaries on plane Couette flow of granular materials: A bifurcation analysis. J Fluid Mech. 1999;397:203–229.
  9. Bocquet L, Losert W, Schalk D, Lubensky TC, Gollub JP. Granular shear flow dynamics and continuum modeling. Phys Rev Lett. 2000;85:5022–5025.
  10. Bocquet L, Errami J, Lubensky TC. Hydrodynamic theory of granular shear flow. Phys Rev E. 2001;65:011307.
  11. Campbell CS. Granular shear flows and microstructure evolution. Powder Technol. 2002;124:1–12.
  12. Goldfarb DJ, Glotzer SC, Goldenfeld N. Instabilities in granular shear flow. Nature. 2002;415:302–305.
  13. Fenistein D, van de Meent JW, van Hecke M. Shear localization in granular materials. Phys Rev Lett. 2003;92:094301.
  14. Kadanoff LP. Built upon sand: Theoretical ideas in granular flow. Rev Mod Phys. 1999;71:435–444.
  15. Howell D, Behringer RP, Veje C. Fluctuations in granular Couette flow. Phys Rev Lett. 1999;82:5241–5244.
  16. Mueth DM, Jaeger HM, Nagel SR. Force chains in granular shear flow. Nature. 2000;406:385–389.
  17. Jop P, Forterre Y, Pouliquen O. A constitutive law for dense granular flows. Nature. 2006;441:727–730.
  18. Khain E, Meerson B. Shear instability in granular flows. Phys Rev E. 2006;73:061301.
  19. Olmsted PD. Shear banding in complex fluids. Rheol Acta. 2008;47:283–300.
  20. Shukla P, Alam M. Weakly nonlinear instability in granular Couette flow. J Fluid Mech. 2011;666:204–253.
  21. Krishnaraj KP, Nott PR. A dilation-driven vortex flow in sheared granular materials explains a rheometric anomaly. Nat Commun. 2016;7:10630.
  22. Dsouza PV, Nott PR. A non-local constitutive model for slow granular flow that incorporates dilatancy. J Fluid Mech. 2020;914:A36.
  23. Dsouza PV, Nott PR. Dilatancy-driven secondary flows in dense granular materials. J Fluid Mech. 2021;914:A36.
  24. Nott PR. Cosserat and nonlocal granular continuum theories. J Fluid Mech. 2000–2021;457, 914.
  25. Mandal S, et al. Continuum theory for dense granular flows with nonlocal effects. Phys Rev X. 2021;11:021017.
  26. Dhooge A, Govaerts W, Kuznetsov YA. MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans Math Softw. 2003;29(2):141–164.
  27. Kuznetsov YA. Elements of Applied Bifurcation Theory. 2nd ed. New York: Springer; 1998.
  28. Govaerts WJF. Numerical Methods for Bifurcations of Dynamical Equilibria. Philadelphia: SIAM; 2000.
  29. Hart WE, Laird CD, Watson JP, Woodruff DL, Hackebeil GA, Nicholson BL, Siirola JD. Pyomo – Optimization Modeling in Python. 2nd ed. Vol. 67. Cham: Springer; 2017.
  30. Wächter A, Biegler LT. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program. 2006;106:25–57.
Ahead of Print Subscription Original Research
Volume 13
03
Received 06/07/2026
Accepted 05/08/2026
Published 12/08/2026
Publication Time 37 Days

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