For incompressible flow models, the pressure term serves as a Lagrange multiplier to ensure that the incompressibility constraint is satisfied. In engineering applications, the pressure term is necessary for calculating important quantities based on stresses like the lift and drag. For reduced order models (ROMs) generated via a Proper Orthogonal Decomposition (POD), it is common for the pressure to drop out of the equations and produce a velocity-only ROM. To recover the pressure, many techniques have been numerically studied in the literature; however, these techniques have undergone little rigorous analysis. In this talk, we explore several ways to recover the pressure using both strictly incompressible and non-incompressible data. Theoretical stability and convergence results for these different approaches are presented. Additionally, numerical results confirming the theoretical analysis will be shown.
Thackeray Hall 427