Mathematics

Numerical stabilization techniques are frequently employed to mitigate the arising of spurious oscillations, a common occurrence in simulations of convection-dominated flows modelled by the incompressible Navier-Stokes equations, particularly in under-resolved or marginally-resolved regimes.This talk aims to present and analyze a novel regularized reduced order model (Reg-ROM) based on approximate deconvolution, ADL-ROM. In the first part of this talk, I introduce a well-known Reg-ROM for the incompressible Navier-Stokes equations, i.e., L-ROM, and our new one, i.e., ADL-ROM. In L-ROM a differential filter is used to smooth the numerical oscillations that arise in the Galerkin ROM (G-ROM) for large Reynolds numbers in the under-resolved regime. In ADL-ROM, the purpose is to deconvolve the filtered variable in L-ROM to increase its accuracy without compromising its stability.In the second part of the talk, we comment on and compare these Reg-ROMs with each other and with G-ROM by showing: ADL-ROM numerical results, the comparison between the different ROMs, and the analysis of the errors.In the end, I provide some suggestions about our ongoing work, i.e., proving the stability and convergence of the ADL-ROM. We illustrate these numerical analysis results in the numerical simulation of convection-dominated flows.