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Navier–Stokes Equations vs. ψ–Hamzah Equation: Superiority Analysis

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Bibliographic Details
Title: Navier–Stokes Equations vs. ψ–Hamzah Equation: Superiority Analysis
Authors: JALALI, SEYED RASOUL
Publisher Information: Zenodo, 2025.
Publication Year: 2025
Subject Terms: Navier-Stokes, ψ-Hamzah, fluid dynamics, fractional derivatives, memory-aware fields, ψ-time, turbulence, Reynolds number, convergence speed, data fitting, stability, noise resistance, non-linear flows, boundary layers, non-local interactions, chaotic systems, multi-scale systems, fluid flow modeling, turbulent flows, computational fluid dynamics, fractional calculus, mathematical modeling, memory dynamics, complex systems, chaos theory, Navier-Stokes superiority, ψ-Hamzah equation, fractional-order models, advanced fluid mechanics, turbulence modeling, boundary-dominated flows, fluid dynamics equations, high Reynolds number, numerical simulations, theoretical analysis, fluid flow simulation, memory effects, ψ-Hamzah model advantages, complex network modeling, turbulent fluid dynamics, fractal behavior, non-linear equations, non-ideal fluid dynamics, ψ-Hamzah theory, cognitive modeling, fractal field interactions, engineering simulations, complex network systems, modeling of turbulent systems, physics of fluids, chaotic behavior modeling, ψ-Hamzah equation superiority, high-dimensional flows, fluid stability analysis, numerical methods in fluid dynamics, mathematical physics, time-dependent dynamics, predictive modeling, scientific simulations, advanced computational methods, mathematical fluid dynamics, system theory, cognitive fluid dynamics, biophysical modeling, economic system modeling, multi-disciplinary simulations, memory-driven systems, fluid mechanics breakthroughs, ψ-Hamzah fluid model, field memory modeling, high-performance computing, multi-scale fluid modeling, nonlinear fluid models, engineering fluid dynamics, turbulence prediction, ψ-Hamzah applications, advanced computational modeling, turbulence equation modeling, data-driven modeling, ψ-Hamzah analysis, complex system behavior, hydrodynamic simulations, chaos in fluid dynamics, theoretical fluid mechanics, future fluid dynamics research, fractal dynamics, computational physics, fluid dynamics research, memory models, fractal fluid behavior, advanced turbulence models, system dynamics modeling, multi-dimensional fluid systems, non-local fluid equations, high-dimensional systems, memory effects in fluids, systems with memory, turbulent model comparison, ψ-Hamzah turbulence, boundary behavior modeling, non-linear fluid equations, fractal fluid systems, chaos in fluid modeling, cognitive fluid theory, complex fluid dynamics, system modeling, fractal theory in fluid dynamics, chaos in fluid systems, modeling complex phenomena, fluid model analysis, non-local behavior in fluid systems, mathematical modeling in fluid dynamics, fluid memory systems, fluid flow prediction, physics of turbulence, fractal-based equations, computational fluid physics, field memory dynamics, non-local systems, turbulence simulation techniques, high-performance fluid modeling, nonlinear flow simulation, memory in computational systems, engineering fluid equations, future of fluid modeling, advanced fluid dynamics, fluid memory fields, chaos modeling in physics, fractal-based turbulence modeling, system modeling and dynamics, high-dimensional turbulence
Description: This paper presents a comprehensive comparative analysis of the classical Navier–Stokes equations and the novel ψ–Hamzah equation in fluid dynamics, highlighting the superior performance of the ψ–Hamzah model in various critical areas. The Navier–Stokes equations, while foundational in fluid mechanics, are limited by their assumptions of linearity, locality, and instantaneous field behavior. In contrast, the ψ–Hamzah equation incorporates fractional derivatives, memory-aware fields, and ψ–time, offering a more robust framework for modeling complex, non-linear, and turbulent fluid flows. Through numerical simulations and theoretical analysis, we demonstrate that the ψ–Hamzah model significantly outperforms the classical Navier–Stokes equations in key aspects such as prediction accuracy, data fitting, stability, and resistance to numerical noise. The ψ–Hamzah model is shown to maintain stability even in high Reynolds number regimes (Re ≈ 10⁴), whereas the classical model tends to diverge beyond Re > 3000. Moreover, the ψ–Hamzah model exhibits faster convergence rates and a better match to experimental data, particularly in turbulent and boundary-dominated flows. The superiority of the ψ–Hamzah equation lies not only in its numerical and analytical capabilities but also in its conceptual framework. By redefining time, memory, and field interactions, it provides a more comprehensive understanding of fluid dynamics, especially in chaotic, non-linear, and multi-scale systems. The model’s capacity to adapt to complex systems with memory dynamics, such as turbulent fluid flow, complex networks, and even fields of cognitive and economic dynamics, positions it as a versatile tool for advancing scientific and engineering simulations across diverse disciplines. This work paves the way for the application of ψ–Hamzah in broader areas, including cosmology, biophysics, economics, and cognitive sciences, where traditional models face significant challenges. The ψ–Hamzah equation offers a more flexible and insightful framework for modeling systems with non-local, time-dependent, and fractal-like behaviors, thus representing a major leap forward in the study and simulation of complex systems.
Document Type: Other literature type
DOI: 10.5281/zenodo.15880468
Rights: CC BY
Accession Number: edsair.doi...........ffbf6acccccd0f37c5967e36d97466b4
Database: OpenAIRE
Description
Abstract:This paper presents a comprehensive comparative analysis of the classical Navier–Stokes equations and the novel ψ–Hamzah equation in fluid dynamics, highlighting the superior performance of the ψ–Hamzah model in various critical areas. The Navier–Stokes equations, while foundational in fluid mechanics, are limited by their assumptions of linearity, locality, and instantaneous field behavior. In contrast, the ψ–Hamzah equation incorporates fractional derivatives, memory-aware fields, and ψ–time, offering a more robust framework for modeling complex, non-linear, and turbulent fluid flows. Through numerical simulations and theoretical analysis, we demonstrate that the ψ–Hamzah model significantly outperforms the classical Navier–Stokes equations in key aspects such as prediction accuracy, data fitting, stability, and resistance to numerical noise. The ψ–Hamzah model is shown to maintain stability even in high Reynolds number regimes (Re ≈ 10⁴), whereas the classical model tends to diverge beyond Re > 3000. Moreover, the ψ–Hamzah model exhibits faster convergence rates and a better match to experimental data, particularly in turbulent and boundary-dominated flows. The superiority of the ψ–Hamzah equation lies not only in its numerical and analytical capabilities but also in its conceptual framework. By redefining time, memory, and field interactions, it provides a more comprehensive understanding of fluid dynamics, especially in chaotic, non-linear, and multi-scale systems. The model’s capacity to adapt to complex systems with memory dynamics, such as turbulent fluid flow, complex networks, and even fields of cognitive and economic dynamics, positions it as a versatile tool for advancing scientific and engineering simulations across diverse disciplines. This work paves the way for the application of ψ–Hamzah in broader areas, including cosmology, biophysics, economics, and cognitive sciences, where traditional models face significant challenges. The ψ–Hamzah equation offers a more flexible and insightful framework for modeling systems with non-local, time-dependent, and fractal-like behaviors, thus representing a major leap forward in the study and simulation of complex systems.
DOI:10.5281/zenodo.15880468