Seminar by Masayuki Yano

Speaker

Masayuki Yano (University of Toronto)

Title

Model reduction of parametrized aerodynamics problems: error estimation, adaptivity, and nonlinear approximations

Date

  • February 21, 2023 16:00 CET+0100 (Europe/Rome)

  • February 21, 2023 10:00 EST-0500 (US/Eastern)

  • February 21, 2023 09:00 CST-0600 (US/Central)

  • February 21, 2023 07:00 PST-0800 (US/Pacific)

Abstract

We present goal-oriented model reduction of parametrized nonlinear PDEs, with an emphasis on aerodynamics problems that exhibit a wide range of scales, unsteadiness, and geometry changes. The key ingredients are as follows: an adaptive high-order discontinuous Galerkin (DG) method, which provides stability for convention-dominated flows and controls error in the snapshots; linear and nonlinear reduced basis (RB) spaces, which provide rapidly convergent approximations of the parametric manifold; the point-wise empirical quadrature procedure (EQP), which provides efficient and reliable hyperreduction; the dual-weighted residual (DWR) method, which provides effective error estimate for both the DG snapshots and reduced-order model (ROM); and an adaptive weak greedy algorithm, which simultaneously adapts the DG spaces, RB spaces, and EQP to meet the user-specified output error tolerance in an automated manner. We demonstrate the framework for parametrized aerodynamics problems modeled by the compressible Euler and Reynolds-averaged Navier-Stokes equations. In the offline stage, the adaptive greedy algorithm enables efficient and automated training of ROMs. In the online stage, the ROMs accelerate the computation by several orders of magnitude and also provide a posteriori error estimates.

Recording

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