Accelerating unsteady aerodynamic simulations using predictive reduced-order modeling

Abstract

Unsteady computational fluid dynamics (CFD) simulations are essential in aerospace engineering because they can provide high-fidelity flow fields to better understand transient physics, such as vortex shedding. However, unsteady full-order CFD simulations must repeatedly march the flow solution with a small time step and are computationally expensive. Reduced-order modeling (ROM) is a powerful approach to alleviate the above issue by decomposing the unsteady flow solutions into spatial modes and temporal coefficients, making the unsteady flow easier to simulate. Existing ROM studies mostly focused on parametric problems that use a large number of simulation samples to train an offline model (parametric ROM). Although the trained model can quickly predict any flow fields within the parameter space, the computational cost for generating the massive unsteady simulation samples is still high, especially when the number of parameters and their ranges increase. To further address the high-cost issue, we develop an efficient predictive ROM approach to accelerate individual unsteady aerodynamic simulations. We use the Galerkin projection approach to reduce the Reynolds-averaged Navier–Stokes equations, along with the discrete empirical interpolation method (DEIM) for decreasing the computation cost for nonlinear terms. In addition, we develop an efficient ROM formulation that correlates the temporal coefficients between the momentum, pressure, and turbulence equations, allowing solving fewer ROM equations at the prediction stage. The intrusive nature of the predictive ROM enables using the first portion of unsteady flow data to accelerate the rest of the simulation; no massive offline samples are needed. We use the stalled turbulent flow over the NACA0012 airfoil as the benchmark and evaluate the predictive ROM's speed and accuracy for challenging non-equilibrium scenarios caused by a large sudden change in flow conditions. The run time ratios between CFD and ROM (including the calculation of basis vectors and projection matrices) range between 13 and 45. The pressure, drag, lift, pitching moment, and flow fields simulated by the ROM approach agree reasonably well with the CFD references at various times. The proposed predictive ROM approach is, in principle, applicable to different airfoil geometries and flow conditions and can be integrated into a design optimization process for accelerating unsteady aerodynamic simulations.