Emerging Trends in Chemical Engineering Review Article
Artificial Intelligence–Assisted Reduced-Order Modeling and Stability Control in Granular Couette Flow
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. A neural network surrogate that is trained to approximate the dominant eigenvalue 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
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