Comparing different stabilization strategies for reduced order modeling of viscoelastic fluid flow problems

This paper presents a computational framework for model order reduction of viscoelastic fluid flows, with a particular focus on the stabilization of the reduced order model (ROM) and the efficient approximation of non-linear terms appearing in the governing equations. We compare three different stabilization approaches, two of which are based on offline stabilization only and one that uses both offline and online stabilization. Two main techniques for the treatment of non-linear terms are examined and compared: the discrete empirical interpolation method, and a reduced quadrature method based on a sparse recovery technique. Numerical experiments are conducted on two benchmark flows such as the flow past a sphere and the 4:1 contraction flow problem. We show that significant speedups can be achieved using offline streamline upwind Petrov–Galerkin stabilization together with hyper-reduction. We also discuss the potential accuracy losses of the ROM that could result from mesh-related issues of the full-order model (FOM) and propose possible remedies.