Finite point solver for the simulation of 2-D laminar incompressible unsteady flows

Model reduction in the back step fluid–thermal problem with variable geometry

“…To begin with, the ROM developed above is applied using the 210 snapshots indicated in section 2 and retaining the 15 most energetic POD modes, calculated using the projection window (19); the residual is calculated using only 50 equispaced points in the projection window (27). Relative errors (in %) on the three figures of merit (namely, the reattachment length, the pressure drop, and the heat flux) at the test points are given in Table 2 as calculated using both HOSVD + interpolation (as described above) and the ROM; see Table 1 for the definition of the test points and the CFD-calculated valúes of the figures of merit.…”

“…Table 2 Relative errors resulting from both HOSVD + interpolation and ROM calculations on the reattachment length, the pressure drop, and the heat flux, using 210 snapshots and 15 modes. POD modes are calculated in the projection window (19) and the residual is calculated from 50 equispaced points in the projection window (27). The mesh used in the CFD calculations is separated into 5 different zones, as plotted in Fig.…”

“…which is the counterpart of the projection window in the virtual geometry that was used above to calcúlate POD modes (cf equation (19) and see Fig. 2).…”

“…The projection window (19) has been chosen such that it (a) covers most of the recirculation bubble attached to the step and (b) avoids the córner región near the upper part of the step, where CFD calculations show the largest localized errors due to a singularity in the velocity gradient. Note that we are not taking the whole fluid domain to calcúlate POD modes, as is usually done in standard POD + Galerkin approaches; this simplification has been explained and checked in reference [13].…”

“…The snapshots are computed with the CFD method presented in [19] and must be representative of the parameter range we intend to cover. Each snapshot gives the steady state of the system for a specific set of valúes of the parameters; the snapshot is defined by the velocity components, pressure, and temperature, namely…”