Reduced-Order Modeling for Parametrized Time-Dependent Navier-Stokes Equations

  • Fischer, Hendrik (Leibniz Universität Hannover, Universite Paris-Saclay)
  • Fau, Amelie (Universite Paris-Saclay)
  • Wick, Thomas (Leibniz Universität Hannover, Universite Paris-Saclay)

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In this presentation, the application of reduced-order modeling to the parametrized, time-dependent, laminar Navier-Stokes equations is addressed. Here, the major goal is to reduce the computational costs by replacing the high-fidelity framework by a low-rank approximation, such that the solution behavior is preserved. Therefore, we utilize projection-based reduced basis methods and conduct the basis generation by means of a POD-greedy sampling. In order to enable the evaluation of quantities of interest the pressure is stabilized by means of a supremizer enrichment. We present numerical results of our framework applied to the benchmark problems of a flow around a cylinder and a backward-facing step flow. We conclude the talk with recent developments and preliminary extensions of our reduced-order model framework.