Submerged Reduced-Order Models for Incompressible Flow around Obstacles

We present a hybrid reduced-order modeling scheme utilizing domain decomposition to simulate Navier-Stokes pipe flow with circular obstacles. In contrast to previous schemes which use a reduced-order model for the full domain, or a series of separate reduced-order models on small-scale unit components which compose the whole domain, our scheme deploys reduced-order models on user-identified subdomains containing obstacles. These user-identified subdomains have the same shape and size, allowing a single simulation of flow around obstacles to provide multiple useful snapshots per time step for training. Principal orthogonal decomposition (POD) is performed on the collection of snapshots to form a suitable low-rank Galerkin basis for each ROM subdomain. We employ discontinuous Galerkin domain decomposition (DG-DD) finite element methods to enforce interface boundary conditions weakly. We demonstrate that this method can approximate Navier-Stokes flow with high accuracy but reduced computational expense in terms of time and memory.