  For a projection-based reduced order model (ROM) of a fluid flow to be stable
and accurate, the dynamics of the truncated subspace must be taken into
account. This paper proposes an approach for stabilizing and enhancing
projection-based fluid ROMs in which truncated modes are accounted for a priori
via a minimal rotation of the projection subspace. Attention is focused on the
full non-linear compressible Navier-Stokes equations in specific volume form as
a step toward a more general formulation for problems with generic
non-linearities. Unlike traditional approaches, no empirical turbulence
modeling terms are required, and consistency between the ROM and the full order
model from which the ROM is derived is maintained. Mathematically, the approach
is formulated as a trace minimization problem on the Stiefel manifold. The
reproductive as well as predictive capabilities of the method are evaluated on
several compressible flow problems, including a problem involving laminar flow
over an airfoil with a high angle of attack, and a channel-driven cavity flow
problem.

Computational Physics;Fluid Dynamics