Oscillations due to the transport of microstructures

Abstract

The aim of this paper is to report some improvements and some numerical tests of a model for convection of microstructures developed by McLaughlin, Papanicolaou and Pironneau ISLAM J. Appl. Math., 45 (1985), pp. 780-797]. This model was obtained by homogenization techniques. In particular, this paper gives a computational indication of the existence of oscillations in a macroscopic flow which evolves from an initial state with two well-separated length scales. This oscillatory behavior was formally predicted by McLaughlin et al. A simplified model including eddy viscosity terms is first obtained: This model is tested for a threedimensional Poiseuille flow in which the mean flow is one-dimensional. Direct simulations and the simulations of the model are compared and good agreement is obtained in the behavior of both the mean velocity field and the kinetic energy of the microstructure.