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 partial differential equations (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 the following: 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.
Masayuki Yano is an associate professor in the Institute for Aerospace Studies at the University of Toronto. He obtained his bachelor’s degree in Aerospace Engineering from Georgia Tech, Master’s degree in Computation for Design and Optimization from MIT, and Ph.D. in Aerospace Computational Engineering from MIT. His research interests lie in the development and assessment of numerical methods for PDEs, with emphasis on adaptive high-order methods, error estimation, model reduction, and data assimilation.