Accelerating Unsteady CFD Simulations Using a Minimum Residual Based Nonlinear Reduced Order Modeling Approach

Abstract

Reduced-order modeling is evaluated as a means to speed up unsteady computational fluid dynamics (CFD) simulations while maintaining the desired level of accuracy. In the reduced order modeling approach, proper orthogonal decomposition (POD) is applied to some computed response time history from a compressible, unsteady CFD solver to compute a set of orthogonal basis vectors. An approximate flow solution for the next time step is predicted by minimizing the unsteady flow solver residual in the space spanned by the POD basis. This is done by solving a non-linear least-squares problem. This approximate flow solution is then used to initialize the flow solver at this time step, aiming to reduce the number of inner iterations of the dual time stepping loop to convergence compared to the conventional choice of initializing with the previous time step solution or an extrapolation in time. This procedure is repeated for all following time steps. Results for the pitching LANN wing at transonic flow conditions show a more than twofold reduction in the number of inner iterations of the flow solver to convergence. Despite the overhead caused by evaluating the reduced-order model (ROM) at every time step, the method results in a 38% savings in computational time without compromising accuracy, thus improving the overall efficiency for unsteady aerodynamics applications. Finally, several means to further improve the performance are also discussed, including updating the POD basis after every new time step.