Energy Retention and Stability Analysis of the Electro-Atomic Rupture (EAR) Model in Multidimensional Flows

Summary of Version 6.0: This version provides a comprehensive and standalone numerical verification of the Electro-Atomic Rupture (EAR) Theory, developed by Ahmet Ünal. The theory suggests that fluid viscosity collapses when kinetic energy exceeds intermolecular potential barriers, resolving the Navier-Stokes singularity problem through a deterministic physical mechanism. What’s New in v6.0: Physical Grounding: A more detailed explanation of the molecular rupture mechanism. 2D Spectral Analysis: Evidence of "spectral flattening," showing that the EAR model preserves energy in high-wavenumber modes (small scales) where classical models exhibit excessive dissipation. Anomaly Resolution: Proof that low-resolution performance declines are numerical artifacts, with the EAR model consistently outperforming classical formulations at higher grid densities ($NX=96+$). Numerical Stability: Demonstration of stable, high-gradient shock formation using Adaptive CFL and Upwind/TVD schemes. Key Results: The EAR model suggests a deterministic alternative to stochastic turbulence modeling, maintaining up to 99% more energy in micro-scale structures compared to classical Navier-Stokes-based solvers, while ensuring physical stability without artificial blow-up.