Design of Spline-Evolutionary Computing Paradigm for Nonlinear Thin Film Flow Model

Area of Science:

• Computational Fluid Dynamics
• Numerical Analysis
• Fluid Mechanics

Background:

• Nonlinear thin film flow (TFF) systems present significant challenges in computational fluid dynamics.
• Second-grade fluid models introduce complex nonlinear second-order differential systems.
• Efficient and accurate numerical methods are crucial for solving these problems.

Purpose of the Study:

• To introduce a novel stochastic numerical computing method for nonlinear TFF systems.
• To exploit polynomial splines and evolutionary computing for discretization and optimization.
• To develop an efficient and reliable solver for complex fluid dynamics scenarios.

Main Methods:

• Utilized the cubic spline approach (CSA) to transform differential equations into nonlinear algebraic equations.
• Formulated a cost function based on mean squared error for optimization.
• Integrated genetic algorithms (GAs) for global search with sequential quadratic programming (SQP) for local search (CSA-GA-SQP).

Main Results:

• The CSA-GA-SQP solver demonstrated efficiency, reliability, stability, and accuracy across various TFF model scenarios.
• Performance was validated through multiple autonomous executions with varying parameters.
• The method proved effective for nonlinear TFF systems with different second-grade and magnetic parameters.

Conclusions:

• The developed CSA-GA-SQP paradigm is a promising and effective numerical solver for nonlinear TFF systems.
• It offers a robust alternative for tackling stiff nonlinear systems in computational fluid dynamics.
• The method's efficiency and accuracy make it suitable for complex fluid dynamics problems.