Schrödinger–Navier–Stokes–π Unified Computational Framework : A Unified Theoretical and Numerical Architecture for Quantum-Coherent Fluid Dynamics Across Physical and Biological Scales

Ndenga, Barack

Published Dec 5, 2025• 0 citations

Abstract

This article introduces a unified model combining the Schrödinger equation, Navier–Stokes dynamics, and π-field coherence into a single computational framework. The approach describes systems where quantum coherence, viscosity, dissipation, and structural curvature coexist at the nanoscale. The framework predicts hybrid transport regimes, coherence-modulated flow, and π-induced quantum potentials. High-order numerical simulations (4th-order finite differences + RK4) demonstrate transitions between quantum-dominant, hybrid, and classical behaviours. To my knowledge, this is the first formulation unifying Schrödinger dynamics, viscous fluid flow, and π-field curvature into one model.

DOI: 10.5281/zenodo.17832285

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