we introduce a method to recover the reduced pressure for Reduced Order Models (ROMs) of incompressible flows. The pressure is obtained as the leastsquares minimum of the residual of the reduced velocity with respect to a dual norm. We prove that this procedure provides a unique solution whenever the fullorder pair of velocitypressure spaces is infsup stable. We also prove that the proposed method is equivalent to solving the reduced mixed problem with reduced velocity basis enriched with the supremizers of the reduced pressure gradients. Optimal error estimates for the reduced pressure are obtained for general incompressible flow equations and specifically, for the transient NavierStokes equations. We also perform some numerical tests for the flow past a cylinder and the liddriven cavity flow which confirm the theoretical expectations, and show an improved convergence with respect to other pressure recovery methods
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Leastsquares pressure recovery in Reduced Order Methods for incompressible flows
Research Group:
Speaker:
Prof. Majdi Azaiez
Institution:
University of Bordeaux, France
Schedule:
Wednesday, November 15, 2023  15:00
Location:
A004
Abstract:
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