RVE-based multiscale modeling for the Navier-Stokes equations: linking continuum and Lattice-Boltzmann models

Pablo Blanco¹; Andrés Valdez¹; Alejandro Clausse²; Raúl Feijóo¹

¹ Laboratório Nacional de Computação Científica; ² Universidad del Centro

doi:10.20906/CPS/CILAMCE2015-0163

Resumo

This work addresses the multiscale modeling of fluid flow in highly involved media based on the concept of Representative Volume Element. Between scales we consider as basic principles for downscaling information the conservation of the velocity vector field and the conservation of the strain rate tensor field. In this context we formulate (i) the problem to be solved in the representative volume element (at fine scale), and (ii) the homogenization formulae for the force-like and the stress-like fields (at coarse scale) which stand for the procedure of upscaling data. Flow equations corresponding to simple fluids are considered at the coarse scale, and the classical Navier-Stokes equations are approximated in the fine scale by using the Lattice-Boltzmann method. Examples of application of flow in permeable media with small obstacles are presented to show the potentialities of the present approach.

Palavras-chave: Complex fluids; Multiscale; Obstacles; Lattice-Boltzmann