Ai-Enhanced Multiscale Modeling Of Buoyancy-Driven Flows In Porous Media Using Navier-Stokes Equations

Abstract

The Boussinesq approximation is a simplification commonly applied in fluid dynamics to model buoyancy-driven flows (natural convection) where density variations are small but significant in the context of gravitational forces. It originates from the work of Joseph Boussinesq in the 19th century and is widely used to approximate the Navier-Stokes equations for incompressible flows with thermal or compositional variations. [1]Two-space singular perturbation is utilised to establish the approximate governing equations for flow of a viscous heat-conducting fluid through a stiff porous material. Gr 1, a Grashof number computed from the length scale of a typical pore radius, reveals that conventional estimations used in the research of flow through porous media are correct. Results demonstrate improved accuracy and scalability compared to traditional single-scale models, offering insights into optimizing fluid flow analyses in porous media. This work contributes to advancing CFD applications in interdisciplinary fields, including environmental science, botany, and biomedical engineering.