Reduced‐order modeling for parametrized time‐dependent Navier‐Stokes equations

Abstract

AbstractIn this work, we apply reduced‐order modeling to the parametrized, time‐dependent, incompressible, laminar Navier‐Stokes equations. The major goal is to reduce the computational costs by replacing the high‐fidelity system by a low‐rank approximation, which preserves the solution behavior. We utilize projection‐based reduced basis methods and carry out the basis generation by POD‐greedy sampling. Both a velocity‐only and a velocity‐pressure reduced‐order model are considered, with the latter stabilized by means of supremizer enrichment. Here, we investigate further reduction possibilities. We present numerical results of the method applied to the benchmark problem of a two‐dimensional flow around a cylinder with physical parametrization.