Advances in the Pseudo-DNS Methodology: Database Construction for the Averaged Inertial Stresses on the Internal RVE

Pseudo Direct Numerical Simulation (pseudo-DNS) is a novel concurrent multiscale methodology which splits the numerical solution into two: the coarse and the fine parts. Here, the coarse scale solution is computed as usual using a relatively coarse mesh but including the pre-computed inertial stresses from the fine-scale solution. To introduce the basis of the method, in this work the pseudo-DNS model is first applied to the classical convection-diffusion problem. Secondly, in the context of Navier-Stokes solutions far from walls, a database for the fine-scale response is constructed. Several DNSsimulations varying the dimensionless tensor Id, which can be reduced to two parameters, are carried out on a Representative Volume Element (internal RVE) to obtain the averaged internal stresses. Numerical results reveal that some critic Id magnitude, named Idc, can be found. The latter allows distinguishing two kinds of fine-scale solutions: steady state or chaotic transient solutions, i.e. with or without instabilities in the fluid. Therefore, a global stability analysis solving generalized eigenvalue problems is also presented in this work to validate the existence and the value of such Idc. Finally, the database is modeled through an artificial neural network to favor its computational implementation.