  To develop a more convenient subgrid-scale (SGS) model that performs well
even in coarse grid cases, we investigate the transport and modeling of SGS
turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows
based on the stabilized mixed model (SMM). In this paper, we try to increase
the convenience of the SMM by replacing the modeled transport equation for the
SGS energy with an algebraic model. The SMM quantitatively adequately predicts
the total turbulent kinetic energy of the direct numerical simulation (DNS)
even in coarse grid cases. For both the filtered DNS (fDNS) and large-eddy
simulation (LES), the statistically averaged production term balances with the
dissipation in the region away from the wall in the SGS energy transport
equation. In contrast, we reveal that the correlation coefficient between the
production and dissipation terms is high for the modeled transport equation in
LES, whereas that for the fDNS is low. Based on the high correlation or local
equilibrium between the production and dissipation observed in the LES, we
demonstrate the reduction of the SMM into a zero-equation SMM (ZE-SMM). We
construct a new damping function based on the grid-scale Kolmogorov length to
reproduce the near-wall behavior of the algebraic model for the SGS energy. The
ZE-SMM provides quantitatively the same performance as the original SMM that
employs the SGS energy transport model. This result suggests that the local
equilibrium model for the SGS energy provides the equivalent performance as the
transport model in wall-bounded turbulent flows even in coarse grid cases.
