Numerical Analysis and Scientific Computing Seminar | Masayuki Yano, Towards rapid and reliable solution of parametrized PDEs: model reduction with applications to aerodynamics

MC 5479 and online talk (for Zoom Link please contact ddelreyfernandez@uwaterloo.ca)  

Speaker

Masayuki Yano, Assistant Professor, University of Toronto Institute for Aerospace Studies

Title

Towards rapid and reliable solution of parametrized PDEs: model reduction with applications to aerodynamics

Abstract

Many engineering tasks, such as design optimization and uncertainty quantification, require rapid and reliable simulation of complex fluid flows for many different configurations. In this talk, we consider projection-based model reduction of parametrized nonlinear PDEs to accelerate the solution of many-query problems by several orders of magnitude, while providing error estimates in predictive settings. The key ingredients are as follows: an adaptive high-order discontinuous Galerkin method, which provides stable and efficient solution of convection-dominated flows; reduced basis spaces, which provide rapidly convergent approximations of the parametric manifolds; the dual-weighted residual method, which provides effective error estimates for quantities of interest; the empirical quadrature procedure, which provides hyperreduction of nonlinear PDEs; and adaptive training algorithms, which train reduced models that meet the user-specified error tolerance in a fully automated manner. We demonstrate the framework for parametrized aerodynamics problems modeled by the compressible Euler and Reynolds-averaged Navier-Stokes equations, with applications to parameter sweep, uncertainty quantification, and data assimilation.