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For incompressible flow models, the pressure term serves as a Lagrangemultiplier to ensure that the incompressibility constraint is satisfied. Inengineering applications, the pressure term is necessary for calculatingimportant quantities based on stresses like the lift and drag. For reducedorder models generated via a Proper orthogonal decomposition, it is common forthe pressure to drop out of the equations and produce a velocity-only reducedorder model. To recover the pressure, many techniques have been numericallystudied in the literature; however, these techniques have undergone littlerigorous analysis. In this work, we examine two of the most popular approaches:pressure recovery through the Pressure Poisson equation and recovery via themomentum equation through the use of a supremizer stabilized velocity basis. Weexamine the challenges that each approach faces and prove stability andconvergence results for the supremizer stabilized approach. We also investigatenumerically the stability and convergence of the supremizer based approach, inaddition to its performance against the Pressure Poisson method.

Error Analysis of Supremizer Pressure Recovery for POD based Reduced Order Models of the time-dependent Navier-Stokes Equations