A High-Order Analytical Extension of the Corrected Smagorinsky Model for Non-Equilibrium Turbulent Flow

TL;DR

This paper introduces a higher-order extension of the corrected Smagorinsky model that improves the accuracy of turbulence simulations, especially in complex, far-from-equilibrium flow regimes, through advanced error estimation and regularity analysis.

Contribution

The study develops a novel high-order formulation of the corrected Smagorinsky model incorporating advanced techniques for error estimation and regularity analysis in non-equilibrium turbulent flows.

Findings

Enhanced energy dissipation representation in turbulence.

Improved numerical stability in complex boundary conditions.

Theoretical validation of the model's accuracy and applicability.

Abstract

This study presents an extension of the corrected Smagorinsky model, incorporating advanced techniques for error estimation and regularity analysis of far-from-equilibrium turbulent flows. A new formulation that increases the model's ability to explain complex dissipative processes in turbulence is presented, using higher-order Sobolev spaces to address incompressible and compressible Navier-Stokes equations. Specifically, a refined energy dissipation mechanism that provides a more accurate representation of turbulence is introduced, particularly in the context of multifractal flow regimes. Furthermore, we derive new theoretical results on energy regularization in multifractal turbulence, contributing to the understanding of anomalous dissipation and vortex stretching in turbulent flows. The work also explores the numerical implementation of the model in the presence of challenging boundary conditions, particularly in dynamically evolving domains, where traditional methods struggle to maintain accuracy and stability. Theoretical demonstrations and analytical results are provided to validate the proposed framework, with implications for theoretical advances and practical applications in computational fluid dynamics. This approach provides a basis for more accurate simulations of turbulence, with potential applications ranging from atmospheric modeling to industrial fluid dynamics.