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

• Autor(a) principal: Santos, Rômulo Damasclin Chaves dos
• Data de Publicação: 2024
• Outros Autores: Sales, Jorge Henrique de Oliveira, Silva, Alice Rosa da
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: The Journal of Engineering and Exact Sciences
• Texto Completo: https://periodicos.ufv.br/jcec/article/view/17579
• topic: Smagorinsky model.; Weak Solution.; Navier–Stokes equations.; Asymptotic Balance.; Modelo de Smagorinsky.; Solução Fraca.; Equações de Navier–Stokes.; Balanço Assintótico.; Modelo de Smagorinsky.; Solución débil.; Ecuaciones de Navier-Stokes.; Modèle Smagorinsky.; Solution faible.; Équations de Navier-Stokes.

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.