A Locally Parametrized Reduced-Order Model for the Linear Frequency Domain Approach to Time-Accurate Computational Fluid Dynamics

For transonic flows governed by the time-accurate Navier–Stokes equations, small, approximately periodic perturbations can be calculated accurately by transition to the frequency domain and truncating the Fourier expansion after the first harmonic. This is referred to as the linear frequency domain (LFD) method. In this paper, a parametric trajectory of reduced order models (ROMs) for the LFD solver is presented. To this end, several local projection–based ROMs, which are essentially specified by suitable low-order subspaces, are computed by the method of proper orthogonal decomposition (POD) in an offline stage. The claimed trajectory is obtained locally by interpolating the given local subspaces considered as sample points in the Grassmann manifold. It is shown that the manifold interpolation technique is subject to certain restrictions. Moreover, it turns out that the application of computing accurate ROMs for the LFD solver requires a special choice of underlying inner product, necessitating a non-Euclidean approach. By exploiting a separable parametric dependency, real-time online performance is achieved. Numerical results are presented for emulating an airfoil in the transonic flow regime under a sinusoidal pitching motion.