Abstract: This research presents the theoretical framework and numerical implementation of the Sexagesimal Harmony Algorithm (SHA), a novel meta-heuristic designed to solve the Incompressible Navier-Stokes Equations (NSE). By integrating ancient Babylonian sexagesimal (base-60) arithmetic with modern Harmony Search (HS) logic, this study proposes a paradigm shift in how rotational and periodic fluid structures are discretized and optimized. The SHA leverages the superior highly composite properties of the number 60 to minimize truncation errors and spectral bias, which are inherent in traditional binary-coded decimal solvers. We introduce the Sexagesimal Staggered Grid (SSG) and the Harmonic Pitch Adjustment (HPA) operator, demonstrating that base-60 alignment provides superior stability and convergence rates for high-Reynolds number flows (Re > 10, 000). Key Features: Harmonic Discretization: A 60-point harmonic stencil that captures sub-grid scale energy transfers more effectively than standard second-order schemes. Pressure-Velocity Coupling: A Sexagesimal Projection Method that enforces the incompressibility constraint through geometric resonance. Stability Analysis: Introduction of the Harmonic CFL (HCFL) condition, allowing for larger time steps in transient simulations without numerical divergence. Performance Benchmarking: Validation against classic test cases, including the Lid-Driven Cavity and the Taylor-Green Vortex decay. Significance: The findings suggest that the SHA significantly reduces computational overhead by accelerating convergence in the pressure-Poisson loop, offering a robust alternative for Large Eddy Simulations (LES) and complex turbulent flow modeling. This work bridges the gap between ethnomathematics and high-performance computing, suggesting that the geometric properties of base-60 arithmetic are uniquely suited for the physics of fluid rotation.
Jorge Alexander López Miranda (2026) studied this question.