Regularized reduced order models for incompressible flows

Numerical simulations of incompressible flows is often computationally expensive. Reduced order modelling (ROM) has emerged in the last decades as a viable option to alleviate the resulting computational demand. In this presentation we discuss a ROM strategy for under-resolved convection-dominated flows based on a novel regularization technique, namely the approximate deconvolution Leray ROM (ADL-ROM). We will present theoretical foundations of the resulting ADL-ROM by means of error bounds. Furthermore, we will show how the proposed ROM can be implemented in FEniCSx and RBniCSx, and discuss some numerical results on benchmark cases.