Global Regularity Numerical Solver for the 3D Navier-Stokes Equations Applying Topological Fractal Brakes and Algebraic Isolation Mechanisms

This paper proposes a next-generation CFD numerical solver that fundamentally resolves the finitetime singularity problem in the 3-dimensional incompressible Navier-Stokes equations. By integrating a topological fractal brake operating at a critical roughness α = 0.5 and an algebraic isolation mechanism in spectral space, energy leakage into unbounded high-frequency modes is strictly blocked. We mathematically prove global regularity by deriving a strict upper energy bound in the Sobolev space H^1, ensuring the existence and uniqueness of strong solutions. Python simulations under high Reynolds numbers (Re =5000, 8000) confirm exact conformity with Kolmogorov’s −5/3 scaling law, establishing a strictly stable, singularity-free architecture for hypersonic flow analysis.