Energy-conserving operator inference for the incompressible Navier-Stokes equations
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In previous works, energy-conserving reduced order models (ROMs) for the incompressible Navier-Stokes equations have been developed in an intrusive way, i.e. the ROM operators are computed by multiplying the full-order model (FOM) operators with the ROM basis. In many real-world applications access to these FOM operators is not possible, so we need an alternative, non-intrusive approach. One such non-intrusive approach is operator inference: The intrusive ROM operators are approximated using FOM snapshot data. However, the physical structure present in the intrusive ROM operators is generally not preserved in the non-intrusive operators obtained via operator inference. We present an approach that guarantees the operator inference to preserve the skew-symmetry of the convection operator. Thereby, we reduce the number of degrees of freedom in the optimization of the ROM operators making the approach more time- and data-efficient and ensure that the resulting non-intrusive ROM is stable.
