A pseudo-DNS method for the simulation of incompressible fluid flows with instabilities at different scales

In this work, a new model for the analysis of incompressible fluid flows with massive instabilities at different scales is presented. It relies on resolving all the instabilities at all scales without any additional model, i.e., following the direct numerical simulation style. Nevertheless, the computation is carried out at two levels or scales, termed the coarse and the fine. The fine-scale simulation is performed on representative volume elements providing the homogenized stress tensor as a function of several dimensionless numbers characterizing the flow. Consequently, the effect of the fine-scale instabilities is transferred to the coarse level as a homogenized stress tensor, a procedure inspired by standard multi-scale methods used in solids. The present proposal introduces a new way for the treatment of the flow at the fine scale, simulating not only the coarse scale but also the fine scale with all the necessary detail, but without incurring in the excessive computational cost of the classical DNS. Another interesting aspect of the present proposal is the use of a Lagrangian formulation for convecting the eddies simulated on the fine mesh through the coarse domain. Several examples showing the potentiality of this methodology for the simulation of homogeneous flows are presented.