The Maseeh Mathematics and Statistics Colloquium Series*
Jeff Borggaard, Ph.D.
Reduced-Order Models of Fluids for Fast Simulation
Reduced-order models based on the proper orthogonal decomposition (POD) of Navier-Stokes simulations and Galerkin projection are commonly used as surrogates in design, control, and analysis of fluid systems. However, this approach has a number of limitations. One is that the accuracy of the reduced-basis may not be adequate when the model is applied at parameter values different from those used to generate the original simulation data. A second is that even mild turbulence can slow the decay of singular values in the POD and that to achieve a reasonable model size, a dramatic truncation in the basis is required. However, the influence of the discarded modes on the remaining modes must be treated with additional modeling.
In this talk, we discuss procedures to overcome these limitations. Computing derivatives of the POD basis with respect to parameters, such as the Reynolds number, allows us to expand the range of flows that canbe modeled. This includes at least an order of magnitude in relative accuracy for nearby parameter variations as well as more effective prediction of dynamical system properties such as the Strouhal number. Additionally, we propose models motivated by modern large eddy simulation (LES) closure models (variational multiscale and dynamic subgridscale models) along with an efficient two-level implementation to better represent mildly turbulent 3D flow past a cylinder at Reynolds number 1000.
Finally, we will report on our progress in developing reduced-ordermodels for the airflow in buildings. These models may lead to incorporating airflow considerations earlier in the building control and design cycle.
This is joint work with Sunil Ahuja, Imran Akhtar, Gene Cliff, Serkan Gugercin, Alexander Hay, Traian Iliescu, Christopher Jarvis, Zhu Wang, and Lizette Zietsman.
Friday, October 18th, 2013 at 3:15 p.m.
Neuberger Hall room 454
(Refreshments served at 3:00 in presentation room)
* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU. This event is free and open to the public.