  The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear
model reduction method that operates on fully discretized computational models.
It achieves dimension reduction by a Petrov--Galerkin projection associated
with residual minimization; it delivers computational efficency by a
hyper-reduction procedure based on the `gappy POD' technique. Originally
presented in Ref. [1], where it was applied to implicit nonlinear
structural-dynamics models, this method is further developed here and applied
to the solution of a benchmark turbulent viscous flow problem. To begin, this
paper develops global state-space error bounds that justify the method's design
and highlight its advantages in terms of minimizing components of these error
bounds. Next, the paper introduces a `sample mesh' concept that enables a
distributed, computationally efficient implementation of the GNAT method in
finite-volume-based computational-fluid-dynamics (CFD) codes. The suitability
of GNAT for parameterized problems is highlighted with the solution of an
academic problem featuring moving discontinuities. Finally, the capability of
this method to reduce by orders of magnitude the core-hours required for
large-scale CFD computations, while preserving accuracy, is demonstrated with
the simulation of turbulent flow over the Ahmed body. For an instance of this
benchmark problem with over 17 million degrees of freedom, GNAT outperforms
several other nonlinear model-reduction methods, reduces the required
computational resources by more than two orders of magnitude, and delivers a
solution that differs by less than 1% from its high-dimensional counterpart.
