| Fri, Mar 01, 2019
|
Computational and Applied Math Seminar
12:30 PM
HS 004 | | Data meets PDEs: New approaches to parameter recovery and data assimilation in the Navier-Stokes equations
Adam Larios, University of Nebraska
Host: Jiahong Wu
| | | Abstract: In accurately simulating turbulent flows, two major difficulties arise before the simulation even begins; namely the problem of determining the initial state of the flow, and the problem of estimating the parameters. Data assimilation helps to resolve the first problem by eliminating the need for complete knowledge of the initial state. It mixes observational data with the underlying equations, improving accuracy far beyond the total accuracy of pure data methods or pure PDE methods. Recently, a promising new data assimilation algorithm (the AOT algorithm) has been proposed by Azoani, Olson, and Titi, which uses a feedback control term to incorporate observations analytically at the PDE level. This talk is focused on using the AOT algorithm to resolving the second problem of parameter estimation. Namely, using only measurements of the flow, we propose a new algorithm to be run in tandem with the AOT algorithm to estimate the fluid viscosity (equivalently, Reynolds number) on the fly. We will present this algorithm and related algorithms, theorems related to its analysis, and possible applications to subgrid scale modeling. Much of the talk will be accessible to students who have seen only ordinary differential equations. |
|
|
|