A Conservative, Anti-Symmetrized Regularization Solver for 3D Navier-Stokes (Stable over 500k time-steps without blow-up)
Hi everyone,
I’ve been working as an independent researcher on an alternative regularized framework for the 3D incompressible Navier-Stokes equations, focusing on mitigating high-energy convective blow-ups while structurally enforcing global energy conservation laws.
Instead of using traditional subgrid models or smoothing techniques, I introduced a modified convective operator T\_reg(u) based on a strictly anti-symmetrized tensor architecture, embedded with a high-gradient dynamic attenuation factor Gamma(u). By definition, this guarantees that the energy inner product strictly equals zero unconditionally, preserving the structural L2 stability bound.
To back the analytical proof, I wrote a high-precision pseudo-spectral (FFT) Python solver to monitor long-term simulation stability.
Numerical Validation Results:
\- Identity Check: Verified the algebraic condition across 1,000 randomized chaotic configurations down to pure machine precision (< 10\^-13).
\- Ultra-Long Term Simulation: Integrated the time-dependent system over 500,000 steps without a single hint of numerical divergence or NaN error. The kinetic energy decays monotonically and smoothly.
\- Ideal MHD Stress Test: Tested the same operator under absolute zero-viscosity conditions for 10,000 steps. The solver successfully absorbed the hyper-turbulent coupling without numerical collapse.
The full project is hosted on GitHub under a GNU GPL v3.0 license:
GitHub Repository: https://github.com/
I'm sharing this here to get your thoughts and technical feedback. Let me know what you think!