Applied Math Colloquium | Masayuki Yano, Model reduction for transonic aerodynamics: nonlinear approximation, error estimation, and adaptation

MC 5501

Speaker

Masayuki Yano (University of Toronto)

Title

Model reduction for transonic aerodynamics: nonlinear approximation, error estimation, and adaptation

Abstract

Many engineering tasks, such as database generation, design optimization, and uncertainty quantification, require simulation of complex flows for many different configurations. In this talk, we consider projection-based model reduction of parametrized partial differential equations (PDEs), with an emphasis on transonic aerodynamics flows governed by the compressible Euler and Reynolds-averaged Navier-Stokes equations. Our goal is to accelerate the solution of many-query problems by several orders of magnitude while ensuring accuracy. The key ingredients are the following: an adaptive high-order discontinuous Galerkin method, which provides efficient full-order model (FOM) solutions; nonlinear reduced approximation spaces, which incorporate transformed solution snapshots to effect rapidly converging approximation of parametric solution manifolds with slowly decaying Kolmogorov n-width; the dual-weighted residual method, which provides effective error estimates for the FOM and reduced-order model (ROM); and adaptive training algorithms, which construct the FOM and ROM that meet the user-specified error tolerance in an automated manner. We demonstrate the framework for parametrized aerodynamics problems governed by the Euler and RANS equations, with applications to flight parameter sweep, uncertainty quantification, and data assimilation.