A Particle-Derived Nonlinear Dynamical Framework for Bubble Oscillations: Reduced-Order Modeling, Bifurcation Analysis, and Optimal Stabilization

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Year : 2026 | Volume : 13 | Issue : 02 | Page :
By

Lakshmi. N. Sridhar,

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

Abstract

Particle-based fluid simulation has emerged as a powerful computational framework for modeling complex multiphase flows involving large deformations, moving interfaces, and nonlinear fluid interactions that challenge conventional mesh-based approaches. In this work, a nonlinear dynamical systems framework is developed for particle-resolved bubble oscillations by constructing a reduced-order model that preserves the dominant physical mechanisms governing bubble interface evolution. The formulation represents the bubble dynamics through coupled radial and shape deformation modes derived from particle-based fluid behavior, incorporating inertial effects, viscous dissipation, capillary restoring forces, and nonlinear mode coupling. The resulting low-dimensional model provides an efficient representation of particle-resolved dynamics while enabling analytical investigation of stability transitions and oscillatory behavior. Bifurcation analysis identifies critical operating conditions associated with the emergence of nonlinear oscillations, including multiple Hopf bifurcations and the formation of stable limit cycles. Furthermore, an optimal control framework is developed using the Weber number as a physically meaningful control parameter to minimize bubble deformation and promote stable operation. The proposed methodology establishes a connection between high-fidelity particle-based simulations and reduced-order nonlinear analysis, providing a computationally efficient approach for understanding, predicting, and controlling complex multiphase fluid phenomena. The framework offers a pathway toward next-generation particle-based simulations integrated with stability analysis and intelligent control strategies for advanced fluid engineering applications.

Keywords: Particle-based fluid simulation, Smoothed Particle Hydrodynamics (SPH), Bubble dynamics, Reduced- order modeling, Nonlinear stability analysis

[This article belongs to Recent Trends in Fluid Mechanics ]

How to cite this article: Lakshmi. N. Sridhar. A Particle-Derived Nonlinear Dynamical Framework for Bubble Oscillations: Reduced-Order Modeling, Bifurcation Analysis, and Optimal Stabilization. Recent Trends in Fluid Mechanics. 2026; 13(02):-.
How to cite this URL: Lakshmi. N. Sridhar. A Particle-Derived Nonlinear Dynamical Framework for Bubble Oscillations: Reduced-Order Modeling, Bifurcation Analysis, and Optimal Stabilization. Recent Trends in Fluid Mechanics. 2026; 13(02):-. Available from: https://journals.stmjournals.com/rtfm/article=2026/view=255418

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Regular Issue Subscription Review Article
Volume 13
Issue 02
Received 22/08/2026
Accepted 09/09/2026
Published 12/09/2026
Publication Time 21 Days

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