Model reduction for nonlinear aerodynamics and aeroelasticity using a Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of Computational Fluid Dynamics (CFD) solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpolation points by<br/>a discrete empirical interpolation method (DEIM). The flow field is then reconstructed using a least square approximation of the flow modes extracted<br/>by proper orthogonal decomposition (POD). The aeroelastic reduce order<br/>model (ROM) is completed by introducing a nonlinear mapping function<br/>between displacements and the DEIM points. The proposed model is investigated to predict the aerodynamic forces due to forced motions using<br/>a N ACA 0012 airfoil undergoing a prescribed pitching oscillation. To investigate aeroelastic problems at transonic conditions, a pitch/plunge airfoil<br/>and a cropped delta wing aeroelastic models are built using linear structural models. The presence of shock-waves triggers the appearance of limit<br/>cycle oscillations (LCO), which the model is able to predict. For all cases<br/>tested, the new ROM shows the ability to replicate the nonlinear aerodynamic forces, structural displacements and reconstruct the complete flow<br/>field with sufficient accuracy at a fraction of the cost of full order CFD<br/>model.