Model reduction on 2-D incompressible laminar flows: Application on the flow over a backward-facing step

The computation of fluid mechanics problems usually leans on a discretization of the Navier-Stokes equations which has to be so fine that the dimensions of the linear systems to be solved are very high. As a direct consequence, the Central Processing Unit time needed to solve complex systems my become extremely large when accuracy is demanded. When coupling numerical modeling schemes to inversion or control problems, the size of linear systems to be solved has to be drastically reduced. Within this context, the identification method consists in identifying the components of a low-order matrix system. The identification process works as an inverse problem of parameter estimation. The test case shows the ability of the proposed method to reduced with accuracy a particular fluid mechanics problem.