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For a projection-based reduced order model (ROM) of a fluid flow to be stableand accurate, the dynamics of the truncated subspace must be taken intoaccount. This paper proposes an approach for stabilizing and enhancingprojection-based fluid ROMs in which truncated modes are accounted for a priorivia a minimal rotation of the projection subspace. Attention is focused on thefull non-linear compressible Navier-Stokes equations in specific volume form asa step toward a more general formulation for problems with genericnon-linearities. Unlike traditional approaches, no empirical turbulencemodeling terms are required, and consistency between the ROM and the full ordermodel from which the ROM is derived is maintained. Mathematically, the approachis formulated as a trace minimization problem on the Stiefel manifold. Thereproductive as well as predictive capabilities of the method are evaluated onseveral compressible flow problems, including a problem involving laminar flowover an airfoil with a high angle of attack, and a channel-driven cavity flowproblem.

journal of computational physics

Minimal subspace rotation on the Stiefel manifold for stabilization and  enhancement of projection-based reduced order models for the compressible  Navier-Stokes equations