Design Optimization of Fluid Mechanical Systems using Reduced Order Models

Matthew Zahr, Stanford University

High-fidelity physics-based simulations have become an integral component in many fields of science and engineering to gain insight into the complex nature of many physical systems. However, due to the large computational cost required by these simulations, in terms of wall time and resources, they have not emerged as a key player in two particular engineering applications: many-query and real-time analyses. Model reduction is a reduction of the dimension of the simulation at hand in an attempt to reduce the computational cost of high-fidelity simulations. Model reduction can be broken down into two phases: an offline phase where the reduced order model (ROM) is built, and an online phase where the ROM is exploited, possibly many times with many different parameter configurations.

In this poster, we are mainly concerned with the many-query application – in particular, design optimization. In the context of optimization, the online phase consists of exploiting the ROM as we use a well-established optimization technique to search the design space.

We present a method for constructing ROMs via optimal sampling, which is an efficient query of the parameter space in the offline phase in an attempt to decrease the offline cost and increase the parametric robustness of the ROM in the online phase.

We consider two steady nozzle flow problems: one governed by potential equations and the other by the Euler equations. The shape of the nozzle is parameterized by cubic splines and the goal of the optimization is parameter estimation.

Abstract Author(s): Matthew J. Zahr, David Amsallem, and Charbel Farhat