A mathematical analysis to the approximate weak solution of the Smagorinsky Model for different flow regimes

Rômulo Damasclin Chaves dos Santos; Jorge Henrique de Oliveira Sales; Alice Rosa da Silva

doi:10.18540/jcecvl10iss01pp17579

Authors

Rômulo Damasclin Chaves dos Santos Departament of Physics, Technological Institute of Aeronautics, São Paulo, Brazil https://orcid.org/0000-0002-9482-1998
Jorge Henrique de Oliveira Sales State University of Santa Cruz – Department of Exact Sciences, Ilhéus, Bahia, Brazil https://orcid.org/0000-0003-1992-3748
Alice Rosa da Silva Federal University of Uberlândia – UFU, Center for Exact Sciences and Technology, Faculty of Civil Engineering, Uberlândia, Minas Gerais, Brazil

DOI:

https://doi.org/10.18540/jcecvl10iss01pp17579

Keywords:

Smagorinsky model., Weak Solution., Navier–Stokes equations., Asymptotic Balance.

Abstract

This study delves into the numerical approximation of non-stationary Navier-Stokes equations within turbulent regimes, employing the Smagorinsky Model (SM). By treating the model as inherently discrete, we implement a semi-implicit time discretization using the Euler method. This approach includes comprehensive stability analyses, applicable to a spectrum of flow regimes, and an exploration of the asymptotic energy balance dynamics during fluid movements. The primary contribution of this study is found in its methodical approach to the numerical approximation of non-stationary Navier-Stokes equations within turbulent regimes using the Smagorinsky Model (SM). The adoption of a semi-implicit time discretization with the Euler method, coupled with a meticulous analysis of energy balance, establishes a robust foundation adaptable to diverse flow conditions.