A Statistical-Signature Framework for Detecting Irreducible Stochasticity in CFD Simulations

This study proposes a statistical-signature framework for diagnosing when a Computational Fluid Dynamics (CFD) simulation enters a regime where deterministic grid convergence becomes fundamentally unattainable. Traditional Verification & Validation (V&V) methods assume monotonic convergence toward a true solution, an assumption that fails in transitional turbulence, separation-induced unsteadiness, and broadband vortex dynamics.

To address this limitation, the present work introduces two dynamical hypotheses for fluid regimes—(A) reducible deterministic attractor regimes and (B) irreducibly stochastic cascade regimes—and derives three statistical indicators from the enstrophy time series. These indicators are combined through Fisher’s method to generate a unified risk metric for determining whether deterministic convergence is physically meaningful.

This framework provides an a priori diagnostic tool that complements GCI-based approaches and helps engineers assess whether LES, DNS, or experimental validation is necessary.