Using Automatic Differentiation to Create a Nonlinear Reduced-Order-Model Aerodynamic Solver

A novel nonlinear reduced-order-modeling technique for computational aerodynamics and aeroelasticity is presented. The method is based on a Taylor series expansion of a frequency-domain harmonic balance computational fluid dynamic solver residual. The first- and second-order gradient matrices and tensors oft he Taylor series expansion are computed rising automatic differentiation via FORTRAN 90/95 operator overloading. A Ritz-type expansion using proper orthogonal decomposition shapes is then used in the Taylor series expansion to create the nonlinear reduced-order model. The nonlinear reduced-order-modeling technique is applied to a viscous flow about an aeroelastic NLR 7301 airfoil model to determine limit cycle oscillations. Computational times are decreased from hours to seconds using the nonlinear reduced-order model.