An Efficient Zeta-Variable Proper Orthogonal Decomposition-Based Reduced-Order Model for Compressible Flows with Aeroelastic Applications
Abstract
This dissertation presents an efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for use in compressible fluid flows. The method is made efficient by rewriting the governing equations of fluid dynamics using zeta-coordinates, i.e., using primitive variables with specific volume substituted in for density. This substitution allowed for the pre computation of the inner products, or coefficients, of the reduced-order model system of equations, and reduced the nonlinearity of the system. To stabilize the POD-based ROM, three methods were used: (1) the penalty method, (2) artificial dissipation, and (3) a new method that modifies the number of modes used in the POD approximation. Energy-based stabilizing methods to calculate the parameters in the penalty method and the artificial dissipation method were developed to improve the robustness of these methods for predicting new flow solutions. Furthermore, a minimization method to calculate the parameter in the penalty method was also developed.
The POD-based ROM was used to predict solutions for several cases of varying degrees of unsteadiness: for an outlet pressure oscillation and for deforming boundaries. The results of these cases are shown for a quasi-one-dimensional nozzle, a two-dimensional channel, a three-dimensional axisymmetric nozzle, NASA Rotor 67, the 10th standard configuration, and the 11th standard configuration. A stability analysis was performed using Lyapunov's method, and showed that the stabilizing methods used were successful in stabilizing the POD-based ROM. To compare the speedup attained by the POD-based ROM, its CPU time was compared to the full CFD solver, or full-order model, and to a ROM that uses density instead of specific volume. The POD-based ROM attained a speedup of greater than four orders of magnitude when compared to both, and was able to accurately predict new flow solutions.
Citation
Krath, Elizabeth Hope (2021). An Efficient Zeta-Variable Proper Orthogonal Decomposition-Based Reduced-Order Model for Compressible Flows with Aeroelastic Applications. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /193105.