Finite Element Analysis of Pressure-Driven Laminar Flow Inside Periodically Staggered Arrays

Abstract

This work applies a finite element method (FEM) approach with periodic boundary conditions to the Navier- Stokes equations for an incompressible fluid moving inside a planar hexagonally-arranged domain. We highlight the usability of a model which decomposes the total pressure into a linear part and a periodic component to ensure the maintenance of mass flow across the domain. Besides, we apply a strategy to eliminate degrees of freedom directly inside the global matrix, so enforcing the periodicity for Dirichlet and Neumann conditions accordingly. Numerical simulations under low Reynolds number are presented for staggered and nonstaggered array configurations. Additionally, the periodic implementation is verified in contrast to the classical analytical solution of a Taylor vortex, thus providing good representation of the flow desired.