  A novel hyper-reduction method is proposed that conserves kinetic energy and
momentum for reduced order models of the incompressible Navier-Stokes
equations. The main advantage of conservation of kinetic energy is that it
endows the hyper-reduced order model (hROM) with a nonlinear stability
property. The new method poses the discrete empirical interpolation method
(DEIM) as a minimization problem and subsequently imposes constraints to
conserve kinetic energy. Two methods are proposed to improve the robustness of
the new method against error accumulation: oversampling and Mahalanobis
regularization. Mahalanobis regularization has the benefit of not requiring
additional measurement points. Furthermore, a novel method is proposed to
perform structure-preserving temporal localization with the principle interval
decomposition: new interface conditions are derived such that energy and
momentum are conserved for a full time-integration instead of only during
separate intervals. The performance of the new structure-preserving
hyper-reduction methods and the structure-preserving temporal localization
method is analysed using two convection-dominated test cases; a shear-layer
roll-up and two-dimensional homogeneous isotropic turbulence. It is found that
both Mahalanobis regularization and oversampling allow hyper-reduction of these
test cases. Moreover, the Mahalanobis regularization provides comparable
robustness while being more efficient than oversampling.
